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\(L_{2} - L_{\infty }\) filtering for Markovian jump systems with time-varying delays and partly unknown transition probabilities. (English) Zbl 1243.62118
Summary: This paper considers the \(L_{2} - L_{\infty }\) filtering problem for Markovian jump systems. The systems under consideration involve time-varying delays, disturbance signals and partly unknown transition probabilities. The aim of this paper is to design a filter, which is suitable for exactly known and partly unknown transition probabilities, such that the filtering error system is stochastically stable and a prescribed \(L_{2} - L_{\infty }\) disturbance attenuation level is guaranteed. By using the Lyapunov-Krasovskii functional, sufficient conditions are formulated in terms of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed main results. All these results are expected to be of use in the study of filter design for Markovian jump systems with partly unknown transition probabilities.

MSC:
62M20 Inference from stochastic processes and prediction
60G35 Signal detection and filtering (aspects of stochastic processes)
15A45 Miscellaneous inequalities involving matrices
65C60 Computational problems in statistics (MSC2010)
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