Geodesic
Exponential $H_{\infty }$ filter design for stochastic Markovian jump systems with both discrete and distributed time-varying delays
Kybernetika, Tome 50 (2014) no. 4, pp. 491-511

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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.
DOI : 10.14736/kyb-2014-4-0491
Classification : 93B36, 93E03
Keywords: stochastic systems; distributed time-varying delay; $H_{\infty }$ filter; linear matrix inequality 
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     title = {Exponential $H_{\infty }$ filter design for stochastic {Markovian} jump systems with both discrete and distributed time-varying delays},
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Ma, Li; Xu, Meimei; Jia, Ruting; Ye, Hui. Exponential $H_{\infty }$ filter design for stochastic Markovian jump systems with both discrete and distributed time-varying delays. Kybernetika, Tome 50 (2014) no. 4, pp. 491-511. doi: 10.14736/kyb-2014-4-0491

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