Parameter-Dependent Lyapunov Functions for Robust Performance of Uncertain Systems

Abstract

Abstract This paper addresses the H2 robust analysis problem for linear time-invariant continuous and discrete-time systems. New linear matrix inequality conditions are proposed for H2 robust analysis in both cases. The proposed conditions stem from a Lyapunov function that considers an augmented state vector containing, for continuous-time systems, higher order state derivatives and, for discrete-time systems, higher order state shifts. The Lyapunov matrix depends on the uncertain system matrices and also on the polynomial structure imposed to a set of matrices used in the analysis problem. Examples borrowed from the literature illustrate the performance, in terms of scalar decision variables and LMI rows, of the proposed method when compared to other approaches.