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Stability analysis for discrete-time switched systems with unstable subsystems by a mode-dependent average dwell time
Hongbin Zhang1, Dehua Xie2, Hongyu Zhang2
1School of Automation, Nanjing University of Science and Technology, Nanjing, Jiangsu 210049, China; School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China.
ISA Transactions
|June 14, 2014
Summary
New stability conditions for discrete-time switched systems with unstable subsystems are presented. The multiple Lyapunov functions method and mode-dependent average dwell time techniques ensure exponential stability even with fast switching.
Area of Science:
- Control Systems Engineering
- Systems Theory
- Applied Mathematics
Background:
- Discrete-time switched systems are crucial in modern control applications.
- Ensuring stability in systems with unstable subsystems presents significant challenges.
- Existing methods often yield conservative results for complex switched systems.
Purpose of the Study:
- To develop novel and less conservative stability criteria for discrete-time switched systems.
- To address the stability analysis of systems incorporating unstable subsystems.
- To extend the applicability of stability analysis to scenarios with both slow and fast switching.
Main Methods:
- Utilizing the multiple Lyapunov functions (MLFs) method for stability analysis.
- Employing mode-dependent average dwell time (MDADT) techniques.
- Formulating stability conditions as numerically feasible linear matrix inequalities (LMIs).
Main Results:
- New stability conditions derived are less conservative than existing approaches.
- Demonstrated exponential stability for discrete-time switched systems with unstable subsystems.
- The proposed method is effective under both slow and fast switching schemes.
Conclusions:
- The developed MLFs and MDADT-based LMI conditions provide a powerful tool for analyzing switched systems.
- The approach successfully handles unstable subsystems, a key limitation in prior work.
- The findings offer practical implications for designing robust discrete-time control systems.
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