Controllability

Controllability

1. Irrelevant output equation

   • y(t) = Cx(t) + Du(t)

2. LTI system represented by equation of states

   • Initial state
     • x0=x(t0)
   • Final state
     • xtf=x(tf)
   • Time finite
   • x(t) = Ax(t) + Bu(t)

3. test of controllability

   • The dimensional pair (A; B) is controllable
   • The controllability matrix (C)
     • Det(C)≠0
   • Array range
     • Range of C equals n
   • The best known are those of Gilbert and Kalman

4. Output controllability

   • Matrix S with a rank equal to m