31
(1) If p < q the pair (A, B) is not controllable
(2) If m < q the pair (A, K2) is not observable
Proof: The proofs to properties (1) and (2) are similar so we only
prove (1). This will be accomplished by showing the existence of a row
vector v' such that
v'[XI A B] = 0
(2-50)
for some x which is an eigenvalue of A.
From the structure of A, it is apparent that x is an eigenvalue of
C and hence there is a row vector w' such that
w'CxI C] = 0
(2-51)
Now define a matrix Q e Rclx