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Quasi-time-dependent H∞ Control for Discrete-time Switched Systems With Time-varying Delay and Unstable Modes

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Abstract

The issues of stability, l2-gain analysis and H∞ control are addressed for a class of discrete-time switched systems subject to time-varying delay and unstable modes in this paper. To solve the problems, firstly, a hybrid mode-dependent average dwell time (HMDADT) switching strategy is designed by combining slow/fast switching strategy to cope with stable and unstable modes. And improved reciprocally convex combination inequality method is adopted to deal with time-varying delay. Then, by constructing a quasi-time-dependent (QTD) Lyapunov-Krasovskii functional (LKF) with triple sum, new sufficient criteria for global uniform asymptotic stability and l2-gain analysis of the constructed systems are presented. Moveover, based on the above results, a set of QTD H∞ controllers are designed to ensure that the corresponding closed-loop system is globally uniformly asymptotically stable (GUAS) with a prescribed weighted H∞ performance. The QTD controllers designed in this paper are less conservative than the time-independent ones. Finally, two examples are carried out to demonstrate the effectiveness and validity of the developed results.

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Authors and Affiliations

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

    Xiaomin Liu, Baowei Wu, Yue-E Wang & Lili Liu

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  1. Xiaomin Liu
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  2. Baowei Wu
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Correspondence to Baowei Wu.

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This work was supported in part by the National Natural Science Foundation of China under Grant 62273218, in part by the Fundamental Research Funds for the Central Universities under Grant GK202206013, and in part by the Natural Science Basic Research Plan in Shaanxi Province of China under Grant 2021JM208.

Xiaomin Liu received her B.E. degree in measurement and control technology and instrumentation from the Taiyuan University of Science Technology, Taiyuan, China, in 2020. She is currently pursuing an M.S. degree in Shaanxi Normal University. Her current research interests include switched systems, robust control, and static output feedback control.

Baowei Wu received his B.Sc. and M.Sc. degrees in mathematics from Shaanxi Normal University, China, in 1982 and 1985, respectively, a Ph.D. degree in mathematics from Xi’an Jiaotong University, China, in 1998. He is currently a full professor in the School of Mathematics and Statistics from Shaanxi Normal University, Xi’an, China. His current research interests include switched systems, positive systems, fractional order systems, and time delay systems.

Yue-E Wang received her M.S. degree from the College of Mathematics and Information Science from Shaanxi Normal University, Xi’an, China, in 2010, and a Ph.D. degree in control theory and control engineering from Northeastern University, China, in 2014. She is currently an Associate Researcher in the School of Mathematics and Statistics from Shaanxi Normal University, Xi’an, China. Her research interests include switched systems and time delay systems.

Lili Liu received her M.S. degree in applied mathematics from Shaanxi Normal University, Xi’an, China, in 2005 and a Ph.D. degree in applied mathematics from Xi’an Jiaotong University, China, in 2011. She was promoted to associate professor in 2012. She is currently an associate professor in the School of Mathematics and Statistics from Shaanxi Normal University, Xi’an, China. Her research interests include singular systems, switched systems, neural networks, and time delay systems.

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Liu, X., Wu, B., Wang, YE. et al. Quasi-time-dependent H∞ Control for Discrete-time Switched Systems With Time-varying Delay and Unstable Modes. Int. J. Control Autom. Syst. (2024). https://doi.org/10.1007/s12555-022-1085-5

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  • DOI: https://doi.org/10.1007/s12555-022-1085-5

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