On uniform asymptotic stability of switched nonlinear time-varying systems

T. C. Lee, Zhong-Ping Jiang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper is concerned with the study of, both local and global, uniform asymptotic stability for general nonlinear and time-varying switched systems. Two concepts of Lyapunov functions are introduced and used to establish uniform Lyapunov stability and uniform global stability. With the help of output functions, an almost bounded output energy condition and a persistent excitation (PE) condition related to output functions are then proposed and employed to guarantee uniform (global) asymptotic stability. Based on this result, a generalized version of Krasovskii-LaSalle theorem in time-varying switched systems is proposed. Moreover, it is shown that the proposed PE condition can be verified by checking a zero-state observability condition for switched systems with persistent dwell-time. Particularly, our results can be used in the case where only some parts of the overall switched system are stable. It is shown that several existing results in past literature can be covered as special cases using the proposed criteria.

Original languageEnglish (US)
Title of host publicationProceedings of the 2007 American Control Conference, ACC
Pages669-674
Number of pages6
DOIs
StatePublished - 2007
Event2007 American Control Conference, ACC - New York, NY, United States
Duration: Jul 9 2007Jul 13 2007

Other

Other2007 American Control Conference, ACC
CountryUnited States
CityNew York, NY
Period7/9/077/13/07

Fingerprint

Time varying systems
Asymptotic stability
Observability
Lyapunov functions

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Lee, T. C., & Jiang, Z-P. (2007). On uniform asymptotic stability of switched nonlinear time-varying systems. In Proceedings of the 2007 American Control Conference, ACC (pp. 669-674). [4282919] https://doi.org/10.1109/ACC.2007.4282919

On uniform asymptotic stability of switched nonlinear time-varying systems. / Lee, T. C.; Jiang, Zhong-Ping.

Proceedings of the 2007 American Control Conference, ACC. 2007. p. 669-674 4282919.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Lee, TC & Jiang, Z-P 2007, On uniform asymptotic stability of switched nonlinear time-varying systems. in Proceedings of the 2007 American Control Conference, ACC., 4282919, pp. 669-674, 2007 American Control Conference, ACC, New York, NY, United States, 7/9/07. https://doi.org/10.1109/ACC.2007.4282919
Lee TC, Jiang Z-P. On uniform asymptotic stability of switched nonlinear time-varying systems. In Proceedings of the 2007 American Control Conference, ACC. 2007. p. 669-674. 4282919 https://doi.org/10.1109/ACC.2007.4282919
Lee, T. C. ; Jiang, Zhong-Ping. / On uniform asymptotic stability of switched nonlinear time-varying systems. Proceedings of the 2007 American Control Conference, ACC. 2007. pp. 669-674
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