Mean Uniformly Stable Function and Its Application to Almost Sure Stability Analysis of Randomly Switched Time-Varying Systems

Liu, Qian, He, Yong and Jiang, Lin ORCID: 0000-0001-6531-2791 (2025) Mean Uniformly Stable Function and Its Application to Almost Sure Stability Analysis of Randomly Switched Time-Varying Systems IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 70 (12). pp. 8258-8265. ISSN 0018-9286, 1558-2523

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Abstract

This article investigates uniform almost sure stability of randomly switched time-varying systems. Mode-dependent indefinite multiple Lyapunov functions (iMLFs) are introduced to assess stability properties of diverse time-varying subsystems. To realize the stability conditions establishment based on iMLFs, we present a novel condition so-called mean uniformly stable function (MUSF) for time-varying parameters of iMLFs’ derivatives. Our approach provides a probabilistic perspective, making iMLFs well-suited for randomly switched time-varying systems. Moreover, the MUSF condition reveals an essential insight: ensuring that each time-varying subsystem remains mean-bounded during its corresponding sojourn time interval is a prerequisite for the almost sure stability of the entire system. In addition, the combination of iMLFs and MUSFs is able to accommodate stability analysis scenarios where some subsystems are unstable or exhibit nonexponential decay. Numerical examples are provided to demonstrate the effectiveness and advantages of our approach.

Item Type:	Article
Uncontrolled Keywords:	Switches, Stability criteria, Power system stability, Numerical stability, Asymptotic stability, Switched systems, Lyapunov methods, Trajectory, Training, Sufficient conditions, Almost sure exponential stability, almost sure uniform asymptotic stability, random process, switched systems, time-varying systems
Divisions:	Faculty of Science & Engineering Faculty of Science & Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	20 Jun 2025 09:16
Last Modified:	16 Jun 2026 13:38
DOI:	10.1109/TAC.2025.3580631
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3193343
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