The guaranteed cost control problem is studied for a class of 2D discrete uncertain systems in the Fornasini–Marchesini state space setting. The uncertainty is assumed to be normbounded. Based on the guaranteed cost controller for 1D differential/difference systems, the notion of the guaranteed cost control problem for 2D discrete systems is proposed. The problem is to design both a staticstate feedback controller and a dynamic output feedback controller such that the closedloop system is asymptotically stable and the closedloop cost function value is not more than a specified upper bound for all admissible uncertainties. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach. A parametrised characterisation of the guaranteed cost controllers is given in terms of the feasible solutions to a certain LMI. Furthermore, a convex optimisation problem is formulated to select the optimal guaranteed cost controller which minimises the upper bound of the closedloop cost function.
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