On the H-two norm of switched systems via homogeneous rational Lyapunov functions

This paper addresses the problem of determining the H-two norm of continuous-time switched linear systems in the case of arbitrary switching. A novel class of Lyapunov functions is proposed, called homogeneous rational Lyapunov functions (HRLFs). It is shown that a sufficient condition for establishing upper bounds of the H-two norm can be given in terms of a linear matrix inequality (LMI) feasibility test by searching for an 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 approach and its advantages with respect to the existing methods.