Robust [formula omitted] performance analysis and synthesis of linear polytopic discrete-time periodic systems via LMIs

Abstract

A particular class of uncertain linear discrete-time periodic systems is considered. The problem of robust stabilization of real polytopic linear discrete-time periodic systems via a periodic state-feedback control law is tackled here, along with H 2 performance optimization. Using additional slack variables and the periodic Lyapunov lemma, an extended sufficient condition of robust H 2 stabilization is proposed. Based on periodic parameter-dependent Lyapunov functions, this last condition is shown to be always less conservative than the more classic one based on the quadratic stability framework. This is illustrated on a numerical example from the literature.