226 SAMPLED-DATA CONTROL SYSTEMS 
(9.13) in the form 
n—-1 
C(z) = > Z[R(s)e™?/)]Z[G(s) e~mt/™9] (9.14) 
m=0 
which may be visualized by aid of the block diagram of Fig. 9.5. This 
figure shows the general case of switch decomposition. 

Fia. 9.5. General case of switch decomposition. 
EXAMPLE 
A simple illustration of the use of the switch-decomposition method 
for the analysis of an open-loop multirate system will be given by con- 
sidering a triple-rate system with a single time-constant plant and a 
step input. That is, for a system like Fig. 9.4, let 

Il 
R(s) = = 
1 
GUS) ig 
T = 1 sec 
iia 
Either from inspection of the figure or from Eq. (9.14) one can obtain 
the output transform as 



1 1 e3/3 e738/3 e28/3 e728/3 
OO) Ae Sem or. eae PaaS 
il e72/3g-1 
S02) aS 
—1/3,—1 
a é VA 
(Ce ae) Uae) 
pl i ++ (er 4- Cae em } 
~ d-290 — e 27) 

(9.15) 
