Robust $$H_{\infty }$$ H ∞ control for 2-D discrete state delayed systems with polytopic uncertainties

Abstract

This paper is concerned with the problem of robust $$H_{\infty }$$ control for two-dimensional (2-D) discrete state delay systems described by the Roesser model, the uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. Both $$H_{\infty }$$ performance analysis and $$H_{\infty }$$ controller design are considered. Firstly, a sufficient condition for $$H_{\infty }$$ disturbance attenuation performance of the uncertain 2-D discrete systems with state delay is developed. Next, a stabilizing state feedback controller is designed such that the resulting closed-loop system is robustly asymptotically stable and has a prescribed level $$\gamma $$ of $$H_{\infty }$$ performance. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.