An LMI Approach to Optimal Guaranteed Cost Control of Uncertain 2-D Discrete Shift-Delayed Systems via Memory State Feedback

This paper deals with the problem of optimal guaranteed cost control via memory state feedback for a class of two-dimensional (2-D) discrete shift-delayed systems in Fornasini–Marchesini (FM) second model with norm-bounded uncertainties. A new criterion for the existence of memory state feedback guaranteed cost controllers is derived, based on the linear matrix inequality (LMI) approach. Moreover, a convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controllers which minimize the upper bound of the closed-loop cost function. Illustrative examples demonstrate the merit of the proposed method in the aspect of conservativeness over a previously reported result.