1. If the state of the system is completely controllable, the poles of the system can be arbitrarily configured by full state feedback realized by all state variables. (Just arrange the poles in the left half plane. )
2. If the state of the system is not completely controllable, as long as the uncontrollable state is stable, the system can still stabilize the system through the feedback of controllable state variables. (that is, let the system calm down).
& gt& gta =[- 1 0 1； 1 -2 1; 0 0 3];
& gt& gtb =[ 1- 1 0]'；
& gt& gtc =[ 1 0 1]；
& gt& gt ranking ([B, A*B, A*A*B])
ans =
2
It is found that the system is not completely controllable, the third state is uncontrollable (because the third behavior of the control matrix is 0), and the number of state matrices is greater than zero, so it is unstable.
Therefore, the system cannot be stabilized by state feedback.