TY - JOUR
T1 - Nice-reachability results for discrete-time linear switched systems with applications to stability under arbitrary switching laws
AU - Monovich Wahrmann, Tal
AU - Margaliot, Michael
PY - 2012
Y1 - 2012
N2 - A powerful approach for analyzing the stability under arbitrary switching of continuous-time switched systems is based on analyzing stability for the 'most unstable' switching law. This approach has been successfully applied to derive nice-reachability-type results for both linear and nonlinear continuous-time switched systems. We develop an analogous approach for discrete-time linear switched systems. We first prove a necessary condition for the 'most unstable' switching law in the form of a discrete-time maximum principle (MP). This MP is in fact weaker than its continuous-time counterpart. To overcome this, we introduce the auxiliary system of a discrete-time linear switched system, and show that regularity properties of time-optimal controls (TOCs) for the auxiliary system imply nice-reachability results for the original discrete-time linear switched system. We derive several new Liealgebraic conditions guaranteeing nice-reachability results. These results, and their proofs, turn out to be quite different from their continuous-time counterparts.
AB - A powerful approach for analyzing the stability under arbitrary switching of continuous-time switched systems is based on analyzing stability for the 'most unstable' switching law. This approach has been successfully applied to derive nice-reachability-type results for both linear and nonlinear continuous-time switched systems. We develop an analogous approach for discrete-time linear switched systems. We first prove a necessary condition for the 'most unstable' switching law in the form of a discrete-time maximum principle (MP). This MP is in fact weaker than its continuous-time counterpart. To overcome this, we introduce the auxiliary system of a discrete-time linear switched system, and show that regularity properties of time-optimal controls (TOCs) for the auxiliary system imply nice-reachability results for the original discrete-time linear switched system. We derive several new Liealgebraic conditions guaranteeing nice-reachability results. These results, and their proofs, turn out to be quite different from their continuous-time counterparts.
UR - http://www.scopus.com/inward/record.url?scp=84874229427&partnerID=8YFLogxK
U2 - 10.1109/CDC.2012.6426723
DO - 10.1109/CDC.2012.6426723
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AN - SCOPUS:84874229427
SN - 0743-1546
SP - 693
EP - 698
JO - Proceedings of the IEEE Conference on Decision and Control
JF - Proceedings of the IEEE Conference on Decision and Control
M1 - 6426723
T2 - 51st IEEE Conference on Decision and Control, CDC 2012
Y2 - 10 December 2012 through 13 December 2012
ER -