On the RMS gain of switched systems via homogeneous rational Lyapunov functions

Abstract

This paper addresses the problem of determining the root mean square (RMS) gain of continuous-time switched linear systems in the case of arbitrary switching. It is shown that a sufficient condition for establishing upper bounds of the RMS gain can be given in terms of a linear matrix inequality (LMI) feasibility test by searching for a homogeneous rational Lyapunov function (HRLF) of any a priori chosen degree. Moreover, it is shown that this condition is also necessary under some assumptions by using HRLF candidates with degree sufficiently large. Some numerical examples illustrate the proposed methodology and the advantages with respect to the existing works.