Robust optimal guaranteed cost control for 2D discrete systems

The guaranteed cost control problem is studied for a class of 2D discrete u ncertain systems in the Fornasini-Marchesini state space setting. The uncer tainty is assumed to be norm-bounded. Based on the guaranteed cost controll er for 1D differential/difference systems, the notion of the guaranteed cos t control problem for 2D discrete systems is proposed. The problem is to de sign both a static-state feedback controller and a dynamic output feedback controller such that the closed-loop system is asymptotically stable and th e closed-loop cost function value is not more than a specified upper bound for ail admissible uncertainties. Sufficient conditions for the existence o f such controllers are derived based on the linear matrix inequality (LMI) approach. A parametrised characterisation of the guaranteed cost controller s is given in terms of the feasible solutions to a certain LMI. Furthermore , a convex optimisation problem is formulated to select the optimal guarant eed cost controller which minimises the upper bound of the closed-loop cost function.