Robust guaranteed cost control for a class of two-dimensional discrete systems with shift-delays

This paper considers the problem of robust guaranteed cost control for uncertain two-dimensional (2-D) discrete shift-delayed systems in Fornasini-Marchesini (FM) second model. The parameter uncertainty is assumed to be norm-bounded. The problem addressed is the design of state feedback controllers such that the closed-loop system is asymptotically stable and an adequate level of performance can be guaranteed for all admissible uncertainties. The cost function with shift-delays is proposed and an upper bound of the cost function is given. 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.