Digital Signal Processing Reference
In-Depth Information
u
(
t
)
y
(
t
)
x
2
(
t
)
x
2
(
t
)
3
5
x
1
(
t
)
x
1
(
t
)
4
2
(a)
v
1
(
t
)
v
1
(
t
)
3
2
u
(
t
)
y
(
t
)
3
v
2
(
t
)
v
2
(
t
)
2
1
Figure 8.9
Simulation diagrams for
Example 8.13.
(b)
A MATLAB Program that performs the matrix multiplications is given by
A=[0 1;-2 -3];B=[0;1];C=[4 5];D=0;T=[1 1;1 2];
sys=ss(A,B,C,D)
[n,d]=ss2tf(A,B,C,D);
Hs=tf(n,d)
[Av,Bv,Cv,Dv]=ss2ss(A,B,C,D,T)
■
For the system in Example 8.13, the simulation diagram for the
x
(
t
)-state vec-
tor is given in Figure 8.3 and is repeated in Figure 8.9(a). The simulation diagram
for the
v
(
t
)-state vector is given in Figure 8.9(b); this diagram satisfies the
equations (8.65). We show later that the transfer functions of the two simulation di-
agrams are equal; however, note the differences in the internal structures.
v
#
(t)-state
