Delay-Dependent Robust <i>H</i><sub>∞</sub> Control for Uncertain 2-D Discrete State Delay Systems Described by the General Model

Abstract

This paper considers the problem of delay-dependent robust optimal H ∞ control for a class of uncertain two-dimensional (2-D) discrete state delay systems described by the general model (GM). The parameter uncertainties are assumed to be normbounded. A linear matrix inequality (LMI)-based sufficient condition for the existence of delay-dependent γ-suboptimal state feedback robust H ∞ controllers which guarantees not only the asymptotic stability of the closed-loop system, but also the H ∞ noise attenuation γ over all admissible parameter uncertainties is established.Furthermore, a convex optimization problem is formulated to design a delay-dependent state feedback robust optimal H ∞ controller which minimizes the H ∞ noise attenuation γ of the closed-loop system. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.