Page 421 - Schaum's Outline of Theory and Problems of Signals and Systems

408 STATE SPACE ANALYSIS [CHAP. 7

(c) By Eq. (7.44) the system function H(z) is given by

7.36. Consider the system in Prob. 7.7. Assume that

Find x[O] and x[l] such that q[2] = 0.

From Eq. (7.23) we have

Thus,

j x[ol
= [: [m + :x[ol]
+
from which we obtain x[O] = - and x[l] = i.

7.37. Consider the system in Prob. 7.7. We observe y[O] = 1 and y[l] = 0 with x[O] = x[l] = 0.
Find the initial state q[O].
Using Eq. (7.1251, we have

Thus,

Solving for ql[Ol and q,[Ol, we obtain