Robust H∞ control for a class of 2-D discrete delayed systems

•We study the H∞ performance and controller design for a class of 2-D discrete uncertain systems with delayed perturbations.•The design of controllers is via state feedback.•Based on the property of perturbations, we utilize the Lyapunov method and some other strategy to establish the results.•Two numerical examples are given to illustrate the effectiveness of the proposed results.

In this paper, we deal with the problem of robust H∞ control for a class of 2-D discrete uncertain systems with delayed perturbations described by the Roesser state-space model (RM). The problem to be addressed is the design of robust controllers via state feedback such that the stability of the resulting closed-loop system is guaranteed and a prescribed H∞ performance level is ensured for all delayed perturbations. By utilizing the Lyapunov method and some results, H∞ controllers are given. The results are delay-dependent and can be expressed in terms of linear matrix inequalities (LMIs). Finally, some numerical examples are given to illustrate the effectiveness of the proposed results.