Chapter 6 5 Theorem:The following statements are equivalent. 1.The n-dimensional pair(A,B)is controllable. 2. The following nxn matrix is non-singular for any t. W0-eBBte de-BBed 3. The following nxnp controllability matrix(Kalman matrix) has rank n(full row rank). C=BAB…A"B] • Theorem: The following statements are equivalent. 1. The n-dimensional pair (A,B) is controllable. 2. The following nn matrix is non-singular for any t. 3. The following nnp controllability matrix (Kalman matrix) has rank n (full row rank). 5 W (t) e BB e dτ e BB e dτ A(t-τ ) T A (t τ) t Aτ T A τ t C T T          0 0 ] 1 C B AB A B  n-  [ Chapter 6