This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Debian) (preloaded format=pdflatex 2026.4.14) 7 MAY 2026 12:03 entering extended mode restricted \write18 enabled. %&-line parsing enabled. **Q3.tex (./Q3.tex LaTeX2e <2023-11-01> patch level 1 L3 programming layer <2024-01-22> ! LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.1 \textbf{Question 3} You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. Overfull \hbox (64.64003pt too wide) in paragraph at lines 1--2 []\OT1/cmr/bx/n/10 Question [] Overfull \hbox (5.74997pt too wide) in paragraph at lines 1--2 \OT1/cmr/bx/n/10 3 [] ! LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3 L e système devient avec $\rho = EI = 1$ et $q(\zeta,t)=0$ : You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no L in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no y in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no t in font nullfont! LaTeX Font Info: Trying to load font information for +cmr on input line 3. LaTeX Font Info: No file cmr.fd. on input line 3. LaTeX Font Warning: Font shape `/cmr/m/n' undefined (Font) using `/cmr/m/n' instead on input line 3. ! Corrupted NFSS tables. wrong@fontshape ...message {Corrupted NFSS tables} error@fontshape else let f... l.3 Le systè me devient avec $\rho = EI = 1$ et $q(\zeta,t)=0$ : This error message was generated by an \errmessage command, so I can't give any explicit help. Pretend that you're Hercule Poirot: Examine all clues, and deduce the truth by order and method. LaTeX Font Warning: Font shape `/cmr/m/n' undefined (Font) using `OT1/cmr/m/n' instead on input line 3. Missing character: There is no m in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no c in font nullfont! LaTeX Font Info: External font `cmex10' loaded for size (Font) <7> on input line 3. LaTeX Font Info: External font `cmex10' loaded for size (Font) <5> on input line 3. Missing character: There is no e in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no : in font nullfont! Overfull \hbox (20.0pt too wide) in paragraph at lines 3--4 [] [] Overfull \hbox (9.44446pt too wide) in paragraph at lines 3--4 \/cmr/m/n/10 ^^Re [] Overfull \hbox (15.72566pt too wide) in paragraph at lines 3--4 \OML/cmm/m/it/10 ^^Z \/cmr/m/n/10 = [] Overfull \hbox (23.69437pt too wide) in paragraph at lines 3--4 \OML/cmm/m/it/10 EI \/cmr/m/n/10 = [] Overfull \hbox (5.00002pt too wide) in paragraph at lines 3--4 \/cmr/m/n/10 1$ [] Overfull \hbox (36.3246pt too wide) in paragraph at lines 3--4 \OML/cmm/m/it/10 q\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P; t\/cmr/m/n/10 ) = [] Overfull \hbox (5.00002pt too wide) in paragraph at lines 3--4 \/cmr/m/n/10 0$ [] ! LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5 \begin{equation} You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. Overfull \hbox (20.0pt too wide) in paragraph at lines 5--5 [] [] ! LaTeX Error: Environment aligned undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6 \begin{aligned} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Misplaced alignment tab character &. l.7 E\dot{x}_{1d}(t) & = D x_{2d}(t),\\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.8 E\dot{x}_{2d}(t) & = -D^T x_{1d}(t)-\phi(L)u(t),\\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.9 y(t) & = -\phi(L)^T x_{2d}(t). I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! LaTeX Error: \begin{equation} on input line 5 ended by \end{aligned}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.10 \end{aligned} Your command was ignored. Type I to replace it with another command, or to continue without it. Overfull \hbox (324.24289pt too wide) detected at line 11 \OML/cmm/m/it/10 E[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) = \OML/cmm/m /it/10 Dx[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )\OML/cmm/m/it/10 ; [] E[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) = \OMS/cmsy/m/n/10 ^^@\OML/cm m/m/it/10 D[]x[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 L\/cmr/m/n/10 )\OML/cmm /m/it/10 u\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )\OML/cmm/m/it/10 ; [] y \/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) = \OMS/cmsy/m/n/10 ^^@\OML/cmm/m /it/10 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 L\/cmr/m/n/10 )[]\OML/cmm/m/it/10 x[]\ /cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )\OML/cmm/m/it/10 : [] ! LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.13 E n multipliant les deux premières équations par $E^{-1}$, on obtient : You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no E in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no x in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no q in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no , in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no b in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no : in font nullfont! Overfull \hbox (20.0pt too wide) in paragraph at lines 13--14 [] [] Overfull \hbox (4.44444pt too wide) in paragraph at lines 13--14 \/cmr/m/n/10 ^^Re [] Overfull \hbox (4.44444pt too wide) in paragraph at lines 13--14 \/cmr/m/n/10 ^^Se [] Overfull \hbox (18.69446pt too wide) in paragraph at lines 13--14 \OML/cmm/m/it/10 E[]$ [] ! LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.15 \begin{equation} You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. Overfull \hbox (20.0pt too wide) in paragraph at lines 15--15 [] [] ! LaTeX Error: Environment aligned undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.16 \begin{aligned} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Misplaced alignment tab character &. l.17 \dot{x}_{1d}(t) & = E^{-1}D x_{2d}(t),\\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.18 \dot{x}_{2d}(t) & = -E^{-1}D^T x_{1d}(t)-E^{-1}\phi(L)u(t). I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! LaTeX Error: \begin{equation} on input line 15 ended by \end{aligned}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.19 \end{aligned} Your command was ignored. Type I to replace it with another command, or to continue without it. Overfull \hbox (269.60913pt too wide) detected at line 20 []\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) = \OML/cmm/m/it/10 E[]Dx[]\/cm r/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )\OML/cmm/m/it/10 ; [] []\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) = \OMS/cmsy/m/n/10 ^^@\OML/cmm/m/it/10 E[]D[] x[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ \OML/cmm /m/it/10 E[]^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 L\/cmr/m/n/10 )\OML/cmm/m/it/10 u \/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )\OML/cmm/m/it/10 : [] ! LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.22 E t, on obtient comme valeurs de $A$, $B$ et $C$ : You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no E in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no , in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no b in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no , in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no : in font nullfont! Overfull \hbox (20.0pt too wide) in paragraph at lines 22--23 [] [] Overfull \hbox (7.50002pt too wide) in paragraph at lines 22--23 \OML/cmm/m/it/10 A$ [] Overfull \hbox (8.0868pt too wide) in paragraph at lines 22--23 \OML/cmm/m/it/10 B$ [] Overfull \hbox (7.86249pt too wide) in paragraph at lines 22--23 \OML/cmm/m/it/10 C$ [] ! LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.24 \begin{equation} You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. Overfull \hbox (20.0pt too wide) in paragraph at lines 24--24 [] [] ! LaTeX Error: Environment bmatrix undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.26 \begin{bmatrix} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Misplaced alignment tab character &. l.27 0 & E^{-1}D \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.28 -E^{-1}D^T & 0 I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! LaTeX Error: \begin{equation} on input line 24 ended by \end{bmatrix}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.29 \end{bmatrix} = Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment bmatrix undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.30 \begin{bmatrix} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Misplaced alignment tab character &. l.31 0 & 0 & 0 & 0 & 114 & 6 & 12 & -2 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.31 0 & 0 & 0 & 0 & 114 & 6 & 12 & -2 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.31 0 & 0 & 0 & 0 & 114 & 6 & 12 & -2 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.31 0 & 0 & 0 & 0 & 114 & 6 & 12 & -2 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.31 0 & 0 & 0 & 0 & 114 & 6 & 12 & -2 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.31 0 & 0 & 0 & 0 & 114 & 6 & 12 & -2 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.31 0 & 0 & 0 & 0 & 114 & 6 & 12 & -2 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.32 0 & 0 & 0 & 0 & -54 & -6 & -2 & 4 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.32 0 & 0 & 0 & 0 & -54 & -6 & -2 & 4 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.32 0 & 0 & 0 & 0 & -54 & -6 & -2 & 4 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.32 0 & 0 & 0 & 0 & -54 & -6 & -2 & 4 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.32 0 & 0 & 0 & 0 & -54 & -6 & -2 & 4 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.32 0 & 0 & 0 & 0 & -54 & -6 & -2 & 4 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.32 0 & 0 & 0 & 0 & -54 & -6 & -2 & 4 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.33 0 & 0 & 0 & 0 & -1188 & -12 & -114 & 6 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.33 0 & 0 & 0 & 0 & -1188 & -12 & -114 & 6 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.33 0 & 0 & 0 & 0 & -1188 & -12 & -114 & 6 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.33 0 & 0 & 0 & 0 & -1188 & -12 & -114 & 6 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.33 0 & 0 & 0 & 0 & -1188 & -12 & -114 & 6 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.33 0 & 0 & 0 & 0 & -1188 & -12 & -114 & 6 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.33 0 & 0 & 0 & 0 & -1188 & -12 & -114 & 6 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.34 0 & 0 & 0 & 0 & -828 & -12 & -54 & 6 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.34 0 & 0 & 0 & 0 & -828 & -12 & -54 & 6 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.34 0 & 0 & 0 & 0 & -828 & -12 & -54 & 6 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.34 0 & 0 & 0 & 0 & -828 & -12 & -54 & 6 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.34 0 & 0 & 0 & 0 & -828 & -12 & -54 & 6 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.34 0 & 0 & 0 & 0 & -828 & -12 & -54 & 6 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.34 0 & 0 & 0 & 0 & -828 & -12 & -54 & 6 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.35 6 & 54 & 4 & -2 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.35 6 & 54 & 4 & -2 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.35 6 & 54 & 4 & -2 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.35 6 & 54 & 4 & -2 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.35 6 & 54 & 4 & -2 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.35 6 & 54 & 4 & -2 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.35 6 & 54 & 4 & -2 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.36 -6 & -114 & -2 & 12 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.36 -6 & -114 & -2 & 12 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.36 -6 & -114 & -2 & 12 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.36 -6 & -114 & -2 & 12 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.36 -6 & -114 & -2 & 12 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.36 -6 & -114 & -2 & 12 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.36 -6 & -114 & -2 & 12 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.37 -12 & -828 & -6 & 54 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.37 -12 & -828 & -6 & 54 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.37 -12 & -828 & -6 & 54 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.37 -12 & -828 & -6 & 54 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.37 -12 & -828 & -6 & 54 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.37 -12 & -828 & -6 & 54 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.37 -12 & -828 & -6 & 54 & 0 & 0 & 0 & 0 \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.38 -12 & -1188 & -6 & 114 & 0 & 0 & 0 & 0 I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.38 -12 & -1188 & -6 & 114 & 0 & 0 & 0 & 0 I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.38 -12 & -1188 & -6 & 114 & 0 & 0 & 0 & 0 I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.38 -12 & -1188 & -6 & 114 & 0 & 0 & 0 & 0 I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.38 -12 & -1188 & -6 & 114 & 0 & 0 & 0 & 0 I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.38 -12 & -1188 & -6 & 114 & 0 & 0 & 0 & 0 I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.38 -12 & -1188 & -6 & 114 & 0 & 0 & 0 & 0 I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! LaTeX Error: \begin{equation} on input line 24 ended by \end{bmatrix}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.39 \end{bmatrix} Your command was ignored. Type I to replace it with another command, or to continue without it. Overfull \hbox (728.30418pt too wide) detected at line 40 \OML/cmm/m/it/10 A \/cmr/m/n/10 = 0\OML/cmm/m/it/10 E[]D[] \OMS/cmsy/m/n/10 ^^ @ \OML/cmm/m/it/10 E[]D[]\/cmr/m/n/10 0 = 0000114612 \OMS/cmsy/m/n/10 ^^@ \/cmr /m/n/10 2[] 0000 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 54 \OMS/cmsy/m/n/10 ^^@ \/cm r/m/n/10 6 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 24[] 0000 \OMS/cmsy/m/n/10 ^^@ \/c mr/m/n/10 1188 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 12 \OMS/cmsy/m/n/10 ^^@ \/cmr/ m/n/10 1146[] 0000 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 828 \OMS/cmsy/m/n/10 ^^@ \ /cmr/m/n/10 12 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 546[] 6544 \OMS/cmsy/m/n/10 ^^ @ \/cmr/m/n/10 20000[] \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 6 \OMS/cmsy/m/n/10 ^^ @ \/cmr/m/n/10 114 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 2120000[] \OMS/cmsy/m/n/1 0 ^^@ \/cmr/m/n/10 12 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 828 \OMS/cmsy/m/n/10 ^^ @ \/cmr/m/n/10 6540000[] \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 12 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 1188 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 61140000 [] ! LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.42 \begin{equation} You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. Overfull \hbox (20.0pt too wide) in paragraph at lines 42--42 [] [] ! LaTeX Error: Environment bmatrix undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.44 \begin{bmatrix} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{equation} on input line 42 ended by \end{bmatrix}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.46 \end{bmatrix} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment bmatrix undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.48 \begin{bmatrix} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: \begin{equation} on input line 42 ended by \end{bmatrix}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.57 \end{bmatrix} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment bmatrix undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.60 \begin{bmatrix} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Misplaced alignment tab character &. l.61 0 & -\Phi^{T}(L,t) I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! LaTeX Error: \begin{equation} on input line 42 ended by \end{bmatrix}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.62 \end{bmatrix} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Environment bmatrix undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.64 \begin{bmatrix} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Misplaced alignment tab character &. l.65 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.65 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.65 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.65 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.65 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.65 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.65 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! LaTeX Error: \begin{equation} on input line 42 ended by \end{bmatrix}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.66 \end{bmatrix} Your command was ignored. Type I to replace it with another command, or to continue without it. Overfull \hbox (302.61017pt too wide) detected at line 67 \OML/cmm/m/it/10 B \/cmr/m/n/10 = 0[] \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 E[ ]\/cmr/m/n/10 ^^H(\OML/cmm/m/it/10 L\/cmr/m/n/10 ) = 0[] 0[] 0[] 0[] 4[] \OMS/ cmsy/m/n/10 ^^@ \/cmr/m/n/10 16[] \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 60[] \OMS /cmsy/m/n/10 ^^@ \/cmr/m/n/10 120 \OML/cmm/m/it/10 C \/cmr/m/n/10 = 0 \OMS/cmsy /m/n/10 ^^@ \/cmr/m/n/10 ^^H[](\OML/cmm/m/it/10 L; t\/cmr/m/n/10 ) = 00000 \OMS /cmsy/m/n/10 ^^@ \/cmr/m/n/10 100 [] Missing character: There is no F in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no , in font nullfont! ! LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.70 \begin{equation} You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. Overfull \hbox (20.0pt too wide) in paragraph at lines 70--70 [] [] ! Undefined control sequence. l.71 \boxed { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: Environment aligned undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.72 \begin{aligned} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Misplaced alignment tab character &. l.73 \dot{x}_d(t) & = Ax_d(t)+Bu(t),\\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. l.74 y(t) & = Cx_d(t). I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! LaTeX Error: \begin{equation} on input line 70 ended by \end{aligned}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.75 \end{aligned} Your command was ignored. Type I to replace it with another command, or to continue without it. Overfull \hbox (168.62527pt too wide) detected at line 77 [] [] ) ! Emergency stop. <*> Q3.tex *** (job aborted, no legal \end found) Here is how much of TeX's memory you used: 40 strings out of 474222 726 string characters out of 5748733 1925975 words of memory out of 5000000 22393 multiletter control sequences out of 15000+600000 558377 words of font info for 37 fonts, out of 8000000 for 9000 1141 hyphenation exceptions out of 8191 23i,3n,32p,114b,91s stack positions out of 10000i,1000n,20000p,200000b,200000s ! ==> Fatal error occurred, no output PDF file produced!