复习]矩阵的线性变换 -PAPHPP-P-APP(I-A)P P-1I(I-A)川P曰P-1IPI(-A)I P-PI(I-A)月(2I-A)川 文=Ar+Bu x=Pz y=Cx+Du School of Mechanical Engineering ME369-lecture 9.1 Shanghai Jiao Tong University Fal12015 能控式的对角化 0 1 0 0 0 0 0 =Ax+Bu= x+ y=Cx 0 0 0 1 -a.-a.1-an-2 4 -41 1 1… 11 P= 房 店 … 无- 「0… 0 A=PAP= 0 B=PB C=CP 0 0 School of Mechanical Engineering ME369-lecture 9.1 Shanghai Jiao Tong University Fall 2015 66 ME369-lecture 9.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [复习]矩阵的线性变换 x   Ax  Bu y  Cx  Du x  Pz | | | | | ( ) | -1 -1 -1 -1 I  P AP  P P  P AP  P I - A P | || ( ) || | | || || ( ) | -1 -1  P I - A P  P P I - A | || ( ) | | ( ) | -1  P P I - A  I - A ME369-lecture 9.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 能控式的对角化 1 2 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 n n n u u a a a a                                           x Ax B x 1 2 2 2 2 1 2 1 1 1 1 2 1 1 1 n n n n n n                              P y  Cx               n          0 0 0 0 0 0 ~ 2 1 -1 A P AP B P B ~ -1  C  CP ~