Page 398 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 71 STATE SPACE ANALYSIS

7.10. Redo Prob. 7.9 by expressing H(z) as

H(z = H,(z)H,(z )

Let

Then we have

W(z) + a,z-'W(z) + ~~z-~W(z) X(z)
=
Y(z) = b,W(z) + b,z-'~(z) + b,z-'~(z)

Rearranging Eq. (7.881, we get
+
W(z) = -a,z-'W(z) - a,~-~~(z) ~(z)
From Eqs. (7.89) and (7.90) the simulation diagram in Fig. 7-9 can be drawn. Choosing the
outputs of unit-delay elements as state variables as shown in Fig. 7-9, we have

ul[n + l] = II~[~]
u,[n + 11 = -a,~!,[n] - a,u,[n] +x[n]
Y [ ~ I = b,u,[nI + b,u,[nI + b,u,[n + 11

= (b2 - boa2)u,[nl+ (61 -b,a,)c2tnI +b&l

Fig. 7-9 Canonical simulation of the second form.