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Sampling of a system with a time delay. (English) Zbl 0561.93041

The paper deals with the problem of sampling a continuous-time system with a time delay. Many processes can be described by a finite dimensional state space system followed by a time delay and then followed by an additional finite dimensional state space system. This means that the time delay can be anywhere in the process. Earlier treatments have assumed that the delay is either on the input or on the output. The case with ”inner” time delay is discussed. Let the sampling period be h and let the time delay be \(\tau =\tau '+(d-1)\) where d is an integer. Explicit expressions for the sampled data system are derived. The necessary expressions are obtained by assuming that \(\tau =0\) and by sampling the system with the sampling periods h, \(\tau\) ’ and h-\(\tau\) ’. This implies that the sampled data representation can be obtained by using standard software for sampling a state space system.

MSC:

93C57 Sampled-data control/observation systems
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
93C05 Linear systems in control theory
93C99 Model systems in control theory
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