K1x1=41K1x2=2…K1x 3证明(A+BK1b)可控 x2=Ab+ Bu,=Ab+ BKX=(A+ BK6 x3=Ax2+ Bu2= Ax2+ BKx2=(A+ BK1x2=(A+ BK1 b Axn- 2+ Bun-2=(A+BKDxn-2=(A+ BK1)b xn= Axn-+ Bum=(A+ BKDxm=(A+ Bkb 因为x12x2…n线性无关,即 rankb(A+BK)6(A+ BK)2b.(A+ BK)b=n1 1 1 1 2 2 1 −1 −1 = = = n n K x u K x u  K x u ( ) 3,证明 A+ BK1 b 可控 x A x Bu A BK x A BK b x A x Bu A BK x A BK b x A x Bu A x BK x A BK x A BK b x A b Bu A b BK x A BK b x b n n n n n n n n n n 1 1 1 1 1 1 2 1 2 2 1 2 1 2 3 2 2 2 1 2 1 2 1 2 1 1 1 1 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) − − − − − − − − − = + = + = + = + = + = + = + = + = + = + = + = + = + =  rankb A BK b A BK b A BK b n n + + + = −1 1 2 1 1 ( ) ( )  ( ) n x , x , , x 因为 1 2  线性无关，即