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 l(p) induced norm sense. By specializing to the Go 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 sufficient conditions for the stability of linear systems with time varying delays.