TY - JOUR
T1 - Analysis and design of switched normal systems
AU - Zhai, Guisheng
AU - Xu, Xuping
AU - Lin, Hai
AU - Michel, Anthony N.
N1 - Funding Information:
The authors would like to thank Prof. Joe Imae and Dr. Tomoaki Kobayashi with Osaka Prefecture University, Prof. Kazunori Yasuda with Wakayama University, for their valuable discussions. This research has been supported in part by the Japan Ministry of Education, Science and Culture under Grants-in-Aid for Scientific Research (B) 15760320 & 17760356.
PY - 2006/12/15
Y1 - 2006/12/15
N2 - In this paper, we study the stability property for a class of switched linear systems whose subsystems are normal. The subsystems can be continuous-time or discrete-time ones. We show that when all the continuous-time subsystems are Hurwitz stable and all the discrete-time subsystems are Schur stable, a common quadratic Lyapunov function exists for the subsystems and thus the switched system is exponentially stable under arbitrary switching. We show that when unstable subsystems are involved, for a desired decay rate of the system, if the activation time ratio between stable subsystems and unstable ones is less than a certain value (calculated using the decay rate), then the switched system is exponentially stable with the desired decay rate.
AB - In this paper, we study the stability property for a class of switched linear systems whose subsystems are normal. The subsystems can be continuous-time or discrete-time ones. We show that when all the continuous-time subsystems are Hurwitz stable and all the discrete-time subsystems are Schur stable, a common quadratic Lyapunov function exists for the subsystems and thus the switched system is exponentially stable under arbitrary switching. We show that when unstable subsystems are involved, for a desired decay rate of the system, if the activation time ratio between stable subsystems and unstable ones is less than a certain value (calculated using the decay rate), then the switched system is exponentially stable with the desired decay rate.
KW - Activation time ratio between stable and unstable subsystems
KW - Arbitrary switching
KW - Common Lyapunov function
KW - Stability
KW - Switched normal system
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U2 - 10.1016/j.na.2006.01.034
DO - 10.1016/j.na.2006.01.034
M3 - Article
AN - SCOPUS:33750974173
VL - 65
SP - 2248
EP - 2259
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
IS - 12
ER -