In this paper, we develop a new framework to analyze stability and stabilizability of Linear Switched Systems (LSS) 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 (LTV) systems, in any l_p induced norm sense. By specializing to the l_∞ case, we show how Linear Programming (LP) can be used to test stability, stabilizability and to synthesize stabilizing controllers that guarantee a near optimal closed-loop gain.