TY - JOUR
T1 - Stability of switched linear discrete-time descriptor systems
T2 - A new commutation condition
AU - Zhai, Guisheng
AU - Xu, Xuping
AU - Ho, Daniel W.C.
N1 - Funding Information:
The authors would like to thank Prof. Masao Ikeda with Osaka University for valuable discussions. This research has been supported in part by the Japan Ministry of Education, Sciences and Culture under Grant-in-Aid for Scientific Research (C) 21560471.
PY - 2012/11/1
Y1 - 2012/11/1
N2 - In this article, we study stability of switched linear discrete-time descriptor systems. Under the assumption that all subsystems are stable and there is no impulse occurring at the switching instants, we establish a new pairwise commutation condition under which the switched system is stable. It turns out that the condition is a natural and important extension to the existing commutation conditions, and it can be applied in discretised continuous-time switched systems in a straightforward manner. Finally, we also show that when the proposed commutation condition holds, there exists a common quadratic Lyapunov function for the subsystems.
AB - In this article, we study stability of switched linear discrete-time descriptor systems. Under the assumption that all subsystems are stable and there is no impulse occurring at the switching instants, we establish a new pairwise commutation condition under which the switched system is stable. It turns out that the condition is a natural and important extension to the existing commutation conditions, and it can be applied in discretised continuous-time switched systems in a straightforward manner. Finally, we also show that when the proposed commutation condition holds, there exists a common quadratic Lyapunov function for the subsystems.
KW - common quadratic Lyapunov functions
KW - impulse-free switching
KW - matrix inequalities
KW - pairwise commutation
KW - stability
KW - switched linear discrete-time descriptor systems
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U2 - 10.1080/00207179.2012.703788
DO - 10.1080/00207179.2012.703788
M3 - Article
AN - SCOPUS:84867026302
SN - 0020-7179
VL - 85
SP - 1779
EP - 1788
JO - International Journal of Control
JF - International Journal of Control
IS - 11
ER -