STATE SPACE ANALYSIS
[CHAP. 7
Fig. 7-1
In matrix form
or
where
7.2.
Redo Prob. 7.1 by choosing the outputs of unit-delay elements 2 and 1 as state ) variables u,[n] and u,[n], respectively, and verify the relationships in Eqs. ( 7 . 1 0 ~and (7. lob). We redraw Fig. 7-1 with the new state variables as shown in Fig. 7-2. From Fig. 7-2 we have
+ 11 = 3 u l [ n ] + 2 u , [ n ] + x [ n ] ~+[ 11 n =c,[n] y [ n ] = 3 u l [ n ] + 2 u 2 [ n ]+ x [ n ]
u,[n ~ l
Fig. 7-2