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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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