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Asynchronous Finite-Time \(H_{\infty }\) Control for Discrete-Time Switched Systems with Admissible Edge-Dependent Average Dwell Time

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Abstract

This paper is concerned with asynchronous finite-time \(H_{\infty }\) control for a class of discrete-time switched linear systems via admissible edge-dependent average dwell time (AED-ADT) approach. Firstly, by considering the switching time delay between the system and the state feedback controller, appropriate Lyapunov functions are constructed for asynchronous and synchronous switching, respectively. Secondly, for the existence of a set of state feedback controllers, a sufficient condition which guarantees the finite-time boundedness of the closed-loop system with AED-ADT is proposed. Thirdly, a sufficient condition for finite-time \(H_{\infty }\) control with a prescribed \(H_{\infty }\) performance is further developed based on the obtained result. Finally, a numerical example is given to verify the validity of the proposed theoretical results.

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Data Availability

The authors declare that the data supporting the findings of this study are available within the article.

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Acknowledgements

The authors are grateful for the support of the National Natural Science Foundation of China (Grant No. 62273218), the Fundamental Research Funds for the Central Universities (Grant No. GK202206013), and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2021JM208).

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  1. School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, 710119, China

    Mengjiao Wang, Baowei Wu, Yue-E. Wang & Lili Liu

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  1. Mengjiao Wang
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Wang, M., Wu, B., Wang, YE. et al. Asynchronous Finite-Time \(H_{\infty }\) Control for Discrete-Time Switched Systems with Admissible Edge-Dependent Average Dwell Time. Circuits Syst Signal Process 42, 4553–4584 (2023). https://doi.org/10.1007/s00034-023-02321-6

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