SAMPLED-DATA SYSTEMS 93 
In the compensation of sampled-data systems by means of digital con- 
trollers, the problem is to determine the D(z) which will produce a 
desired relation between output and input sequences. 
The over-all response pulse transfer functions for other configurations 
are found in a similar manner and are tabulated in Appendix III for ready 
reference. The expressions for any intermediate variables, such as the 
control error, can be found by application of the rules of combination 
given in Sec. 5.1. The time-domain pulse sequences are always obtain- 
able by the use of inversion techniques, so that the transient response at 
the output of a feedback sampled-data system is readily available. 
5.3 Stability of Sampled-data Systems 
As in the case of continuous systems, the objective of the designer of a 
sampled-data system is to obtain characteristics which are outlined in a 

Fig. 5.6. Example of time function with “hidden oscillations.” 
specification. It is always understood without explicit statement that 
the system must be stable. For linear systems this implies that the out- 
put in response to a bounded input must be bounded. For sampled-data 
systems, this criterion is altered slightly to state that a sampled-data sys- 
tem is stable if the output pulse sequence is bounded when the input 
pulse sequence is bounded also. It is recognized that this leaves open 
the possibility that the continuous output may be unbounded by contain- 
ing oscillations of increasing amplitude, though a sample sequence 
derived therefrom may be bounded. This effect is illustrated in Fig. 5.6, 
where it is seen that even though the oscillation is increasing without 
bound, the zero crossovers are synchronous with the sampler. This 
“hidden oscillation’? was introduced by Barker! and studied by later 
investigators,” but as a practical matter this condition rarely arises; and 
if it does it is readily detected. In order to remain undetected in an 
