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Exponential \(H_\infty\) filter design for stochastic Markovian jump systems with both discrete and distributed time-varying delays. (English) Zbl 1309.93146
Summary: This paper is concerned with the exponential \(H_{\infty }\) filter design problem for stochastic Markovian jump systems with time-varying delays, where the time-varying delays include not only discrete delays but also distributed delays. First of all, by choosing a modified Lyapunov-Krasovskii functional and employing the property of conditional mathematical expectation, a novel delay-dependent approach is developed to deal with the mean-square exponential stability problem and \(H_{\infty }\) control problem. Then, a mean-square exponentially stable and Markovian jump filter is designed such that the filtering error system is mean-square exponentially stable and the \(H_{\infty }\) performance of estimation error can be ensured. Besides, the derivative of discrete time-varying delay \(h(t)\) satisfies \(\dot{h}(t)\leq \eta \) and simultaneously the decay rate \(\beta \) can be finite positive value without equation constraint. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design approach.
MSC:
93E03 Stochastic systems in control theory (general)
93B36 \(H^\infty\)-control
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