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

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.