Robust control for a class of uncertain nonlinear two-dimensional systems with state delays

This paper considers the problem of robust H ∞ control for uncertain 2-D discrete state-delayed systems in the Fornasini–Marchesini second local state-space model with a class of generalized Lipschitz nonlinearities. The parameter uncertainty is assumed to be norm-bounded. The problem to be addressed is the design of state feedback controllers such that the stability of the resulting closed-loop system is guaranteed and a prescribed H ∞ performance level is ensured for all admissible uncertainties. In terms of a linear matrix inequality (LMI), a sufficient condition for the solvability of the problem is obtained. A desired state feedback controller can be constructed by solving a certain LMI. A numerical example is provided to demonstrate the application of the proposed method.