[例4]能控式的对角化 0 1 01 001x+0u y=[00 -6-11-66 School of Mechanical Engineering ME369-lecture 9.1 Shanghai Jiao Tong University Fall 2015 齐次状态方程&状态转移矩阵 文=Ax+Bu (t)=ax(t) u(t)=0 x(t)=e"x(0) x(t)=Ax(t)） x(t)=e4x(0) e=1+a++…+a+…=2a 21 k! e=I+At+ 21 k! 该无穷级数在有限时间是绝对收敛的 School of Mechanical Engineering ME369-lecture 9.1 Shanghai Jiao Tong University Fall 2015 77 ME369-lecture 9.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [例4 ] 能控式的对角化 u                          6 0 0 6 11 6 0 0 1 0 1 0 x x y  1 0 0x ME369-lecture 9.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 齐次状态方程& 状态转移矩阵 x Ax B   u u t( ) 0  x Ax ( ) ( ) t t  ( ) (0) at x t e x  x t ax t ( ) ( )  ( ) (0) t t e  A x x         2 2 ! 1 1 1 2! ! ! At k k k k k e I At A t A t A t k k 2 2 0 1 1 1 1 2! ! ! at k k k k k e at a t a t a t k k          该无穷级数在有限时间是绝对收敛的