齐次状态方程&状态转移矩阵（续） e40=I If AB=BA e+)=e·e4 lev]"=err e4-)e4-)=e-) If AB+BA de“=Ae d [e"=e e 0 0 School of Mechanical Engineering ME369-lecture 9.1 Shanghai Jiao Tong University Fal12015 齐次状态方程&状态转移矩阵（续） (t)=Ax(t) |r sX(s)-x(0)=AX(s) X(s)=(sI-A)x(0) IT x(0=L[X(s=E[(sl-A)x(0)] x(①)=e"xo =[(sl-A1x(0) e4=L-[(sI-A)] School of Mechanical Engineering ME369-lecture 9.1 Shanghai Jiao Tong University Fall 2015 88 ME369-lecture 9.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University d t t e e dt  A A A 1 2 1 2 t t t t e e e    A A A ( )1 [ ]t t e e    A A If AB=BA If AB≠BA -1 e e  P AP A P P -1                 1 2 0 0 n A                 1 2 0 0 n t t At t e e e e e  A0 I t n n t [ ] e e  A A t t t t t t e e e     2 1 1 0 2 0 A( ) A A ( ) ( ) 齐次状态方程& 状态转移矩阵（续） ME369-lecture 9.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University x Ax ( ) ( ) t t  s s s X x AX ( ) (0) ( )   LT ( ) ( ) (0) s s  X I A x   1   -1 -1 1 ( ) ( ) ( ) (0) - t L s = L s -      x X I A x ILT -1 L s - ( ) (0)      1 I A x 0 ( ) t t e  A x x [( ) ] t e L s     A I A 1 1 齐次状态方程& 状态转移矩阵（续）