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Delay-range-dependent robust $$H^\infty$$ filtering for uncertain stochastic systems with mode-dependent time delays and Markovian jump parameters. (English) Zbl 1141.93025
Summary: This paper investigates the problem of robust $$H^\infty$$ filtering for uncertain stochastic time-delay systems with Markovian jump parameters. Both the state dynamics and measurement of the system are corrupted by Wiener processes. The time delay varies in an interval and depends on the mode of operation. A Markovian jump linear filter is designed to guarantee robust exponential mean-square stability and a prescribed disturbance attenuation level of the resulting filter error system. A novel approach is employed in showing the robust exponential mean-square stability. The exponential decay rate can be directly estimated using matrices of the Lyapunov-Krasovskii functional and its derivative. A delay-range-dependent condition in the form of LMIs is derived for the solvability of this $$H^\infty$$ filtering problem, and the desired filter can be constructed with solutions of the LMIs. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach.

##### MSC:
 93B36 $$H^\infty$$-control 93E03 Stochastic systems in control theory (general) 93E15 Stochastic stability in control theory
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