On stability, L2L2-gain and H∞H∞ control for switched systems

This paper addresses the issues of stability, L2L2-gain analysis and H∞H∞ control for switched systems via multiple Lyapunov function methods. A concept of general Lyapunov-like functions is presented. A necessary and sufficient condition for stability of switched systems is given in terms of multiple generalized Lyapunov-like functions, which enables derivation of improved stability tests, an L2L2-gain characterization and a design method for stabilizing switching laws. A solution to the H∞H∞ control problem for switched systems is also provided.