Page 414 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 71 STATE SPACE ANALYSIS

Thus, by Eq. (7.34) we get

which is the same result obtained in Prob. 7.27(6).

7.29. Consider the discrete-time system in Prob. 7.7. Assume that the system is initially
relaxed.

(a) Using the state space representation, find the unit step response of the system.
(b) Find the system function H(z).
(a) From the result from Prob. 7.7 we have
q[n + 11 = Aq[n] + bx[n]
Y [ ~ I = cq[nl+ dub1

Setting q[O] = 0 and x[n] = u[n] in Eq. (7.29, the unit step response s[n] is given by

Now, from Prob. 7.20 we have

n-l-k n- l -k
and c~n-'-kb [ 1 4
=

+(f) n-l-k [-s [ -,][,]
0
-4
n- l-k n-k n - k