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Weighted \(\mathbf{H}_\infty\) Performance Analysis of Nonlinear Stochastic Switched Systems: A Mode-Dependent Average Dwell Time Method

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Abstract

In this paper, the issues about weighted \(H_\infty\) performance analysis and \(H_\infty\) control for the stochastic switched nonlinear systems (SSNSs) with multiplicative noise are investigated. The mode-dependent average dwell time (MDADT) method is used to deal with the switching in different modes. Firstly, we get a sufficient condition to show that the considered system with all stable subsystems achieves the exponential stability in mean square sense and a specified weighted \(H_\infty\) performance, which is extended to the case that both stable and unstable subsystems coexist in terms of second-order Hamilton-Jacobi inequalities (HJIs). Then, by using Takagi-Sugeno (T-S) fuzzy approach, the \(H_\infty\) controller for SSNSs is designed via solving a set of linear matrix inequalities (LMIs). Finally, an example is supplied to illustrate the effectiveness of our results.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (61374104, 61773170, 61873099), the Key Laboratory of Autonomous Systems and Networked Control, and the Natural Science Foundation of Guangdong Province of China (2016A030313505).

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Authors and Affiliations

  1. School of Automation Science and Engineering, South China University of Technology, Guangzhou, 510640, Guangdong Province, People’s Republic of China

    Xiushan Jiang & Senping Tian

  2. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266590, Shandong Province, People’s Republic of China

    Weihai Zhang

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  1. Xiushan Jiang
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Correspondence to Senping Tian.

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Jiang, X., Tian, S. & Zhang, W. Weighted \(\mathbf{H}_\infty\) Performance Analysis of Nonlinear Stochastic Switched Systems: A Mode-Dependent Average Dwell Time Method. Int. J. Fuzzy Syst. 22, 1454–1467 (2020). https://doi.org/10.1007/s40815-020-00864-3

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  • DOI: https://doi.org/10.1007/s40815-020-00864-3

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