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Partially mode-dependent design of \(H_{\infty }\) filter for stochastic Markovian jump systems with mode-dependent time delays. (English) Zbl 1219.93134
Summary: This paper is concerned with the \(H_{\infty }\) filtering problem for stochastic delay systems with Markovian jump parameters, where both the state dynamics and measurements of systems are corrupted by Wiener process. In contrast with traditional mode-dependent and mode-independent filtering methods, a new partially mode-dependent filter is established via using a mode-dependent Lyapunov function, where the system mode available to filter implementation is transmitted through an unreliable network and the stochastic property of mode available to a filter is considered. Sufficient conditions for the existence of \(H_{\infty }\) filters are obtained as linear matrix inequalities. Finally, an example is used to show the effectiveness of the given theoretical results.

MSC:
93E11 Filtering in stochastic control theory
93B36 \(H^\infty\)-control
60J75 Jump processes (MSC2010)
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