New Results on Stability of Slowly Switched Systems: A Multiple Discontinuous Lyapunov Function Approach

In this technical note, the problem of stability for a class of slowly switched systems is investigated. By developing a novel multiple discontinuous Lyapunov function approach and exploring the feature of mode-dependent dwell time switching, new stability conditions are established for systems with...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 62; no. 7; pp. 3502 - 3509
Main Authors Zhao, Xudong, Shi, Peng, Yin, Yunfei, Nguang, Sing Kiong
Format Journal Article
LanguageEnglish
Published IEEE 01.07.2017
Subjects
Lyapunov methods
mode-dependent average dwell time
Nonlinear systems
Stability criteria
Switched system
Switched systems
Switches
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Summary:In this technical note, the problem of stability for a class of slowly switched systems is investigated. By developing a novel multiple discontinuous Lyapunov function approach and exploring the feature of mode-dependent dwell time switching, new stability conditions are established for systems with a designed switching strategy where fast switching and slow switching are respectively applied to unstable and stable subsystems. In particular, stability conditions for linear switched systems are also given via choosing multiple discontinuous Lyapunov functions in the quadratic form. Moreover, stability criteria for the systems consisting of stable subsystems are also derived. It is shown that our proposed results cover some existing ones in literature as special cases, and provide tighter bounds on the dwell time. Finally, some simulation results are provided to show the advantages of the theoretic results obtained.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2016.2614911