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.
|Number of pages||6|
|Journal||Proceedings of the IEEE Conference on Decision and Control|
|State||Published - 2012|
|Event||51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States|
Duration: 10 Dec 2012 → 13 Dec 2012