Root-mean-square gains of switched linear systems

In this note, we compute the root-mean-square (RMS) gain of a switched linear system when the interval between consecutive switchings is large. The algorithm proposed is based on the fact that a given constant (gamma) provides an upper bound on the RMS gain whenever there is a separation between the stabilizing and the antistabilizing solutions to a set of (gamma)-dependent algebraic Riccati equations. The motivation for this problem is the application of robust stability tools to the analysis of hybrid systems.