Qualitative analysis of discrete-time switched systems

Guisheng Zhai, Bo Hu, Kazunori Yasuda, Anthony N. Michel

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

179 Citations (Scopus)

Abstract

In this paper, we investigate some qualitative properties for time-controlled switched systems consisting of several linear discrete-time subsystems. First, we study exponential stability of the switched system with commutation property, stable combination and average dwell time. When all subsystem matrices are commutative pairwise and there exists a stable combination of unstable subsystem matrices, we propose a class of stabilizing switching laws where Schur stable subsystems (if exist) are activated arbitrarily while unstable ones are activated in sequence with their duration time periods satisfying a specified ratio. For more general switched system whose subsystem matrices are not commutative pairwise, we show that the switched system is exponentially stable if the average dwell time is chosen sufficiently large and the total activation time ratio between Schur stable and unstable subsystems is not smaller than a specified constant. Secondly, we use an average dwell time approach incorporated with a piecewise Lyapunov function to study the L2 gain of the switched system. We show that when all subsystems are Schur stable and achieve an L2 gain smaller than a positive scalar γ0, (1) if all subsystems have a common Lyapunov function in the sense of L2 gain, then the switched system achieves the same L2 gain γ0 under arbitrary switching; (2) if there does not exist a common Lyapunov function, then the switched system under an average dwell time scheme achieves a weighted L2 gain γ0, and the weighted L2 gain approaches normal L2 gain if the average dwell time is chosen sufficiently large.

Original languageEnglish
Title of host publicationProceedings of the American Control Conference
Pages1880-1885
Number of pages6
Volume3
DOIs
Publication statusPublished - 2002
Externally publishedYes
Event2002 American Control Conference - Anchorage, AK
Duration: 2002 May 82002 May 10

Other

Other2002 American Control Conference
CityAnchorage, AK
Period02/5/802/5/10

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Lyapunov functions
Electric commutation
Asymptotic stability
Chemical activation

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Zhai, G., Hu, B., Yasuda, K., & Michel, A. N. (2002). Qualitative analysis of discrete-time switched systems. In Proceedings of the American Control Conference (Vol. 3, pp. 1880-1885) https://doi.org/10.1109/ACC.2002.1023907

Qualitative analysis of discrete-time switched systems. / Zhai, Guisheng; Hu, Bo; Yasuda, Kazunori; Michel, Anthony N.

Proceedings of the American Control Conference. Vol. 3 2002. p. 1880-1885.

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

Zhai, G, Hu, B, Yasuda, K & Michel, AN 2002, Qualitative analysis of discrete-time switched systems. in Proceedings of the American Control Conference. vol. 3, pp. 1880-1885, 2002 American Control Conference, Anchorage, AK, 02/5/8. https://doi.org/10.1109/ACC.2002.1023907
Zhai G, Hu B, Yasuda K, Michel AN. Qualitative analysis of discrete-time switched systems. In Proceedings of the American Control Conference. Vol. 3. 2002. p. 1880-1885 https://doi.org/10.1109/ACC.2002.1023907
Zhai, Guisheng ; Hu, Bo ; Yasuda, Kazunori ; Michel, Anthony N. / Qualitative analysis of discrete-time switched systems. Proceedings of the American Control Conference. Vol. 3 2002. pp. 1880-1885
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