TY - JOUR
T1 - Analysis of switched normal discrete-time systems
AU - Zhai, Guisheng
AU - Lin, Hai
AU - Xu, Xuping
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 - 2007/4/15
Y1 - 2007/4/15
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 establishing 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 establishing a common quadratic Lyapunov function for all subsystems in the sense of unity L2 gain.
KW - Common quadratic Lyapunov functions
KW - L gain
KW - LMI
KW - Stability
KW - Switched normal systems
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U2 - 10.1016/j.na.2006.02.024
DO - 10.1016/j.na.2006.02.024
M3 - Article
AN - SCOPUS:33846623729
VL - 66
SP - 1788
EP - 1799
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
IS - 8
ER -