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Nonlinear Dynamics

, Volume 79, Issue 1, pp 215–228 | Cite as

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

  • Feng Zhao
  • Qingling Zhang
  • Xinggang Yan
  • Min Cai
Original Paper

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.

Keywords

Stochastic singular fuzzy systems \({H_{\infty }}\) filtering \({\mathrm{e}^{\lambda {t}}}\)-Weighted integral input-to-state stable in mean Fuzzy filter 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Feng Zhao
    • 1
  • Qingling Zhang
    • 1
  • Xinggang Yan
    • 2
  • Min Cai
    • 3
  1. 1.Institute of Systems ScienceNortheastern UniversityShenyangPeople’s Republic of China
  2. 2.School of Engineering and Digital ArtsUniversity of KentCanterburyUK
  3. 3.School of Science, Dalian Jiaotong UniversityDalianPeople’s Republic of China

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