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Stochastic stability and robust control for sampled-data systems with Markovian jump parameters. (English) Zbl 1211.93131
Summary: The problems of stochastic stability and robust control for a class of uncertain sampled-data systems are studied. The systems consist of random jumping parameters described by finite-state semi-Markov process. Sufficient conditions for stochastic stability or exponential mean square stability of the systems are presented. The conditions for the existence of a sampled-data feedback control and a multirate sampled-data optimal control for the continuous-time uncertain Markovian jump systems are also obtained. The design procedure for robust multirate sampled-data control is formulated as linear matrix inequalities (LMIs), which can be solved efficiently by available software toolboxes. Finally, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed techniques.

MSC:
93E14 Data smoothing in stochastic control theory
60K15 Markov renewal processes, semi-Markov processes
93D09 Robust stability
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