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

The issues of stability, l 2 -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 b...

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Published inInternational journal of control, automation, and systems Vol. 22; no. 5; pp. 1511 - 1525
Main Authors Liu, Xiaomin, Wu, Baowei, Wang, Yue-E, Liu, Lili
Format Journal Article
LanguageEnglish
Published Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01.05.2024
Springer Nature B.V
제어·로봇·시스템학회
Subjects
Asymptotic properties
Closed loops
Control
Controllers
Delay
Discrete time systems
Dwell time
Engineering
Feedback control
H-infinity control
Hybrid modes
L2 gain
Mechatronics
Regular Papers
Robotics
Switching
Time dependence
Time varying control
제어계측공학
time-varying delay
controller
unstable mode
MDADT
quasi-time-dependent
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ISSN1598-6446
2005-4092
DOI10.1007/s12555-022-1085-5

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Summary:The issues of stability, l 2 -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 l 2 -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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http://link.springer.com/article/10.1007/s12555-022-1085-5
ISSN:1598-6446
2005-4092
DOI:10.1007/s12555-022-1085-5