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Robust H ∞ Filtering for Uncertain Nonlinear Stochastic Systems with Mode-dependent Time-delays and Markovian Jump Parameters

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Abstract

This paper investigates the problem of robust H ∞ filtering for a class of uncertain nonlinear stochastic time-delay systems with Markovian jump parameters. The system under consideration contains parameter uncertainties, Itô-type stochastic disturbances, unknown nonlinearities as well as time-varying delays, which vary in a range and dependent on the mode of the operation. We aim to design a full-order Markovian jump filter such that, for all admissible uncertainties, the filtering error system is robustly asymptotically stable in the mean square, and a prescribed H ∞ disturbance attenuation level is guaranteed. By using the Lyapunov stability theory and Itô differential rule, some sufficient conditions in terms of linear matrix inequality (LMI) are proposed to guarantee the existence of the desired H ∞ filter. Then, the explicit expressions of the desired filter parameters are given. Illustrative examples are provided to demonstrate the effectiveness and applicability of the proposed method.

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Authors and Affiliations

  1. School of Information Science and Engineering, East China University of Science and Technology, Shanghai, 200237, P.R. China

    Huaicheng Yan & Hongbo Shi

  2. State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, P.R. China

    Huaicheng Yan, Hongbo Shi & Jiujun Cheng

  3. Department of Control Science and Engineering, Tongji University, Shanghai, 200092, P.R. China

    Hao Zhang

  4. Department of Electronic Engineering, The Chinese University of Hong Kong, Shatin N.T., Hong Kong

    Max Q.-H. Meng

  5. Department of Computer Science and Technology, Tongji University, Shanghai, 200292, P.R. China

    Jiujun Cheng

Authors
  1. Huaicheng Yan
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  2. Hao Zhang
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  3. Hongbo Shi
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  4. Max Q.-H. Meng
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  5. Jiujun Cheng
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Corresponding author

Correspondence to Huaicheng Yan.

Additional information

This work is supported by the National Natural Science Foundation of China No. 61004028 and No. 60904015, the Shanghai Pujiang Program No. 10PJ1402800, the Fundamental Research Funds for the Central Universities No. WH1014013, the Foundation of East China University of Science and Technology No. YH0142137, and the Chen Guang project supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation No. 09CG17.

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Yan, H., Zhang, H., Shi, H. et al. Robust H ∞ Filtering for Uncertain Nonlinear Stochastic Systems with Mode-dependent Time-delays and Markovian Jump Parameters. Circuits Syst Signal Process 30, 303–321 (2011). https://doi.org/10.1007/s00034-010-9223-3

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  • DOI: https://doi.org/10.1007/s00034-010-9223-3

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