Robust Stabilization for a Class of Uncertain Nonlinear 2D Systems with State Delays

This paper discusses the problem of robust stabilization for uncertain 2D 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 purpose of the problem to be addressed is to design state feedback controllers such that the resulting closed-loop system is stable for all admissible uncertainties. In terms of a linear matrix inequality (LMI), a sufficient condition for the solvability of the robust stabilization problem is obtained, and a desired state feedback controller can be constructed by solving a certain LMI. A numerical example is provided to demonstrate the effectiveness of the proposed approach.