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\(H_\infty \) filtering for stochastic singular fuzzy systems with time-varying delay

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Abstract

This paper considers the \(H_\infty \) filtering problem for stochastic singular fuzzy systems with time-varying delay. We assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by Ito-type stochastic differential equations. Based on an auxiliary vector and an integral inequality, a set of delay-dependent sufficient conditions is established, which ensures that the filtering error system is \({\mathrm{e}^{\lambda t}}\)-weighted integral input-to-state stable in mean (iISSiM). A fuzzy filter is designed such that the filtering error system is impulse-free, \({\mathrm{e}^{\lambda t}}\)-weighted iISSiM and the \(H_\infty \) attenuation level from disturbance to estimation error is below a prescribed scalar. A set of sufficient conditions for the solvability of the \(H_\infty \) filtering problem is obtained in terms of a new type of Lyapunov function and a set of linear matrix inequalities. Simulation examples are provided to illustrate the effectiveness of the proposed filtering approach developed in this paper.

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Authors and Affiliations

  1. Institute of Systems Science, Northeastern University, Shenyang, Liaoning, 110819, People’s Republic of China

    Feng Zhao & Qingling Zhang

  2. School of Engineering and Digital Arts, University of Kent, Canterbury, Kent, CT2 7NT, UK

    Xinggang Yan

  3. School of Science, Dalian Jiaotong University, Dalian, Liaoning, 116028, People’s Republic of China

    Min Cai

Authors
  1. Feng Zhao
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  2. Qingling Zhang
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  3. Xinggang Yan
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  4. Min Cai
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Correspondence to Qingling Zhang.

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Zhao, F., Zhang, Q., Yan, X. et al. \(H_\infty \) filtering for stochastic singular fuzzy systems with time-varying delay. Nonlinear Dyn 79, 215–228 (2015). https://doi.org/10.1007/s11071-014-1658-9

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  • DOI: https://doi.org/10.1007/s11071-014-1658-9

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