Page 439 - Schaum's Outline of Theory and Problems of Signals and Systems

426 STATE SPACE ANALYSIS [CHAP. 7

7.67. A continuous-time LTI system is described by
3s2 - 1
H(s) =
s3 + 3sZ - s - 2
Write the two canonical forms of state representation for the system.

7.68. Consider the continuous-time LTI system shown in Fig. 7-28.
(a) Find the state space representation of the system with the state variables q,(t) and q2(t)
as shown.
(b) Is the system asymptotically stable?
(c) Find the system function Hts).
(dl Is the system BIBO stable?

y(t) =[I llq(t)
The system is not asymptotically stable.

The system is BIBO stable.

Fig. 7-28

7.69. Find e A' for

(a) Using the Cayley-Hamilton theorem method.