Analysis of switched normal discrete-time systems

Guisheng Zhai, Hai Lin, X. U. Xuping, Joe Imae, Tomoaki Kobayashi

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


In this paper, we study stability and ℒ 2 gain properties for a class of switched systems which are composed of normal discrete-time subsystems. When all subsystems are Schur stable, we show that a common quadratic Lyapunov function exists for all subsystems and that the switched normal system is exponentially stable under arbitrary switching. For ℒ 2 gain analysis, we introduce an expanded matrix including each subsystem's coefficient matrices. Then, we show that if the expanded matrix is normal and Schur stable so that each subsystem is Schur stable and has unity ℒ 2 gain, then the switched normal system also has unity ℒ 2 gain under arbitrary switching. The key .point is to establish a common quadratic Lyapunov function for all subsystems in the sense of unity ℒ 2 gain.

Original languageEnglish
Title of host publicationProceedings of the American Control Conference
Number of pages6
Publication statusPublished - 2005
Externally publishedYes
Event2005 American Control Conference, ACC - Portland, OR, United States
Duration: 2005 Jun 82005 Jun 10


Other2005 American Control Conference, ACC
CountryUnited States
CityPortland, OR



  • Common quadratic lyapunov functions
  • LMI
  • Script L sign gain
  • Stability
  • Switched normal systems

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Zhai, G., Lin, H., Xuping, X. U., Imae, J., & Kobayashi, T. (2005). Analysis of switched normal discrete-time systems. In Proceedings of the American Control Conference (Vol. 6, pp. 3800-3805)