L_p analysis and synthesis of linear switched systems: A unified input-output and state-space approach

In this paper, we develop a new framework to analyze stability and stabilizability of linear switched systems (LSSs) as well as their gain computations. Our approach is based on a combination of state space operator descriptions and the Youla parametrization and provides a unified way for analysis and synthesis of LSS and, in fact of linear time varying systems, in any lp induced norm sense. By specializing to the l1 case, we show linear programming can be used to test stability, stabilizability, and to synthesize stabilizing controllers that guarantee a near optimal closed-loop gain. Furthermore, we extend our results to the general class of linear systems, finite or infinite dimensional. To show the utility of this framework, we develop a set of necessary and suficient conditions for the stability of linear systems with time varying delays.