TY - GEN
T1 - A unified approach to analysis of switched linear descriptor systems under arbitrary switching
AU - Zhai, Guisheng
AU - Xu, Ping
PY - 2009
Y1 - 2009
N2 - We establish a unified approach to stability and ℒ2 gain analysis for switched linear descriptor systems under arbitrary switching in both continuous-time and discrete-time domains. The approach is based on common quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs). We show that if there is a common quadratic Lyapunov function for stability of all subsystems, then the switched system is stable under arbitrary switching. Furthermore, we show that if there is a common quadratic Lyapunov function for stability and certain ℒ2 gain of all subsystems, then the switched system is stable and has the same ℒ2 gain under arbitrary switching. The analysis results are natural extensions of the existing results for switched linear state space systems.
AB - We establish a unified approach to stability and ℒ2 gain analysis for switched linear descriptor systems under arbitrary switching in both continuous-time and discrete-time domains. The approach is based on common quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs). We show that if there is a common quadratic Lyapunov function for stability of all subsystems, then the switched system is stable under arbitrary switching. Furthermore, we show that if there is a common quadratic Lyapunov function for stability and certain ℒ2 gain of all subsystems, then the switched system is stable and has the same ℒ2 gain under arbitrary switching. The analysis results are natural extensions of the existing results for switched linear state space systems.
KW - Arbitrary switching
KW - Common quadratic Lyapunov functions
KW - Linear matrix inequalities (LMIs)
KW - Stability
KW - Switched linear descriptor systems
UR - http://www.scopus.com/inward/record.url?scp=77950799860&partnerID=8YFLogxK
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U2 - 10.1109/CDC.2009.5400699
DO - 10.1109/CDC.2009.5400699
M3 - Conference contribution
AN - SCOPUS:77950799860
SN - 9781424438716
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 3897
EP - 3902
BT - Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Y2 - 15 December 2009 through 18 December 2009
ER -