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Reliable H∞ Filter Design for a Class of Mixed-Delay Markovian Jump Systems with Stochastic Nonlinearities and Multiplicative Noises via Delay-Partitioning Method

Shiping Wen, Zhigang Zeng*, and Tingwen Huang
International Journal of Control, Automation, and Systems, vol. 10, no. 4, pp.711-720, 2012

Abstract : This paper is concerned with the problem of reliable H∞ filter design for a class of mixed-delay Markovian jump systems with stochastic nonlinearities and multiplicative noises. The mixed delays comprise both discrete time-varying delay and distributed delay. The stochastic nonlinearities in the form of statistical means cover several well-studied nonlinear functions. And the multiplicative dis-turbances are in the form of a scalar Gaussian white noise with unit variance. Furthermore, the failures of sensors are quantified by a variable varying in a given interval. A filter is designed to guarantee that the dynamics of the estimation error is asymptotically mean-square stable. Sufficient conditions for the existence of such a filter are obtained by using a new Lyapunov-Krasovskii functional and delay-partitioning method. Then a linear matrix inequality (LMI) approach for designing such a reliable H∞ filter is presented. Finally, the effectiveness of the proposed approach is demonstrated by a numerical example.

Keyword : Delay partitioning, H∞ filter, Markovian jump, multiplicative noise, reliable filtering, stochastic nonlinearity.

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