An extension of lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems

Guisheng Zhai, Xuping Xu, Hai Lin, Derong Liu

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

4 Citations (Scopus)

Abstract

We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show that there is a common quadratic Lyapunov-like function for all subsystems and the switched system is exponentially stable under a dwell time scheme. Two numerical examples are provided to demonstrate the result.

Original languageEnglish
Title of host publicationProceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06
Pages362-367
Number of pages6
Publication statusPublished - 2006
Externally publishedYes
Event2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06 - Ft. Lauderdale, FL
Duration: 2006 Apr 232006 Apr 25

Other

Other2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06
CityFt. Lauderdale, FL
Period06/4/2306/4/25

Fingerprint

Algebra
Lyapunov functions

Keywords

  • Arbitrary switching
  • Common quadratic lyapunov (lyapunov-iike) functions
  • Dwell time scheme
  • Exponential stability
  • Lie algebra
  • Switched systems

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Control and Systems Engineering

Cite this

Zhai, G., Xu, X., Lin, H., & Liu, D. (2006). An extension of lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems. In Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06 (pp. 362-367). [1673173]

An extension of lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems. / Zhai, Guisheng; Xu, Xuping; Lin, Hai; Liu, Derong.

Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06. 2006. p. 362-367 1673173.

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

Zhai, G, Xu, X, Lin, H & Liu, D 2006, An extension of lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems. in Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06., 1673173, pp. 362-367, 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06, Ft. Lauderdale, FL, 06/4/23.
Zhai G, Xu X, Lin H, Liu D. An extension of lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems. In Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06. 2006. p. 362-367. 1673173
Zhai, Guisheng ; Xu, Xuping ; Lin, Hai ; Liu, Derong. / An extension of lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems. Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, ICNSC'06. 2006. pp. 362-367
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