TY - JOUR

T1 - Analysis of switched normal discrete-time systems

AU - Zhai, Guisheng

AU - Lin, Hai

AU - Xuping, X. U.

AU - Imae, Joe

AU - Kobayashi, Tomoaki

N1 - Funding Information:
The authors would like to thank the reviewers for their constructive comments on the paper. This research was supported in part by the Japan Ministry of Education, Sciences and Culture under Grants-in-Aid for Scientific Research (B) 15760320 & 17760356.

PY - 2005

Y1 - 2005

N2 - In this paper, we study stability and ℒ2 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 ℒ2 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 ℒ2 gain, then the switched normal system also has unity ℒ2 gain under arbitrary switching. The key .point is to establish a common quadratic Lyapunov function for all subsystems in the sense of unity ℒ2 gain.

AB - In this paper, we study stability and ℒ2 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 ℒ2 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 ℒ2 gain, then the switched normal system also has unity ℒ2 gain under arbitrary switching. The key .point is to establish a common quadratic Lyapunov function for all subsystems in the sense of unity ℒ2 gain.

KW - Common quadratic lyapunov functions

KW - LMI

KW - Script L sign gain

KW - Stability

KW - Switched normal systems

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M3 - Conference article

AN - SCOPUS:23944489800

VL - 6

SP - 3800

EP - 3805

JO - Proceedings of the American Control Conference

JF - Proceedings of the American Control Conference

SN - 0743-1619

T2 - 2005 American Control Conference, ACC

Y2 - 8 June 2005 through 10 June 2005

ER -