Page 433 - Schaum's Outline of Theory and Problems of Signals and Systems

STATE SPACE ANALYSIS [CHAP. 7

Fig. 7-22

In matrix form

where

Now

and by Eq. (7.128) the controllability matrix is
M,= [b Ab] = [: :]

and lM,I = 0. Thus, its rank is less than 2 and hence the system is not controllable.
(b) Similarly,

and by Eq. (7.133) the observability matrix is

and lMoI = 0. Thus, its rank is less than 2 and hence the system is not observable.
(c) By Eq. (7.52) the system function H(s) is given by
H(S) =c(s~-A)-'~

Note that the system is both uncontrollable and unobservable.