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New Criteria of Robust \(H_\infty \) Stability for Fuzzy Mixed-Delay Systems with Nonlinear Noise Disturbances

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Abstract

This paper investigates new criteria of the robust \(H_\infty \) stability for a class of uncertain stochastic fuzzy mixed-delay systems with nonlinear noise disturbances by employing an improved free-weighting matrix approach. The fuzzy system is based on the Takagi–Sugeno model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning. To reflect more realistic dynamical behaviors of the system, both the parameter uncertainties and stochastic disturbances are considered, the stochastic disturbances are given in the form of a Brownian motion. The mixed delays comprise both discrete and distributed time-varying delays. In terms of a stochastic fuzzy Lyapunov functional, a sufficient criterion is proposed to investigate dynamical behaviors of the system in the mean-square sense with an \(H_\infty \) performance index.

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Author information

Authors and Affiliations

  1. School of Automation, Huazhong University of Science and Technology, Wuhan, 430074, China

    Yuting Cao, Zhigang Zeng & Shiping Wen

  2. Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan, 430074, China

    Yuting Cao, Zhigang Zeng & Shiping Wen

  3. Texas A&M University at Qatar, Doha, 23874, Qatar

    Tingwen Huang

Authors
  1. Yuting Cao
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  2. Zhigang Zeng
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  3. Tingwen Huang
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  4. Shiping Wen
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Corresponding author

Correspondence to Zhigang Zeng.

Additional information

This work was supported by the Natural Science Foundation of China under Grants 61403152 and 61402218, National Basic Research Program of China (973 Program) under Grant 2011CB710606. This publication was made possible by NPRP Grant \(\sharp \)4-1162-1-181 from the Qatar National Research Fund (a member of Qatar Foundation).

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Cao, Y., Zeng, Z., Huang, T. et al. New Criteria of Robust \(H_\infty \) Stability for Fuzzy Mixed-Delay Systems with Nonlinear Noise Disturbances. Circuits Syst Signal Process 35, 2810–2831 (2016). https://doi.org/10.1007/s00034-015-0185-3

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  • DOI: https://doi.org/10.1007/s00034-015-0185-3

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