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Stability Analysis for Digital Redesign of Discrete-Time Switched Systems Using H ∞ Linear Matrix Inequality

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  • Nien-Tsu Hu

    (Graduate Institute of Automation Technology, National Taipei University of Technology, Taipei 10608, Taiwan)

Abstract

In this paper, the stability problem for the digital redesign of discrete-time switched systems using H ∞ linear matrix inequality (LMI) is investigated. We propose the switching time approach for digital redesign between controller work and failure, and this switching time will limit the system output within the system capacity. When the controller fails, the overall system will be unstable. Therefore, if the digital redesign controller is not restored in a certain period of time, the system output will exceed the system capacity. To solve this problem, we propose a switching law to determine the switching time between the stable mode (controller work) and the unstable (controller failure) mode; this will limit the overall system states in the unstable mode. In addition, the digital redesign controller has the advantage of faster tracking. After we propose a discrete-time switching system with stable and unstable modes, we use H ∞ linear matrix inequality (LMI) and Lyapunov functions to prove the stability in detail. Finally, the numerical example illustrates the feasibility of the proposed approach.

Suggested Citation

  • Nien-Tsu Hu, 2023. "Stability Analysis for Digital Redesign of Discrete-Time Switched Systems Using H ∞ Linear Matrix Inequality," Mathematics, MDPI, vol. 11(11), pages 1-22, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2468-:d:1157317
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    References listed on IDEAS

    as
    1. Wang, Ruihua & Jiao, Ticao & Zhang, Tao & Fei, Shumin, 2019. "Improved stability results for discrete-time switched systems: A multiple piecewise convex Lyapunov function approach," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 54-65.
    2. Shuyan Qi & Jun Zhao & Li Tang, 2023. "Adaptive Output Feedback Control for Constrained Switched Systems with Input Quantization," Mathematics, MDPI, vol. 11(3), pages 1-16, February.
    3. Han, Yunrui & Zhao, Ying & Wang, Peng, 2021. "Finite-time rate anti-bump switching control for switched systems," Applied Mathematics and Computation, Elsevier, vol. 401(C).
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