An LMI approach to design robust <i>H</i><SUB align="right">∞ controller for 2-D systems with delays

Abstract

This paper focuses on H∞ controller design for two-dimensional (2-D) discrete state delay systems described by the second Fornasini-Marchesini local state space (FM LSS) model with polytopic uncertainties. The objective is to design a robust state feedback controller such that the corresponding closed-loop system achieves robust asymptotic stability and guarantees a prescribed H∞ performance index for all admissible uncertainties. Based on parameter-dependent Lyapunov functions and Finsler's lemma, a new sufficient condition for H∞ performance analysis of 2-D discrete systems with delays is developed. Then a stabilising state feedback controller is designed. A simulation example is exploited to show the effectiveness of the proposed approach.