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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 norm-bounded. 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 static-state feedback controller and a dynamic output feedback controller such that the closed-loop system is asymptotically stable and the closed-loop 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 closed-loop cost function.
Inspec keywords: closed loop systems; state-space methods; robust control; matrix algebra; minimisation; control system synthesis; uncertain systems; multidimensional systems; asymptotic stability; state feedback; optimal control; convex programming; discrete systems
Other keywords: 1D differential/difference systems; Fornasini-Marchesini state space; 2D discrete uncertain systems; asymptotically stable closed-loop system; LMI; dynamic output feedback controller design; norm-bounded uncertainty; convex optimisation; static-state feedback controller design; closed-loop cost function upper bound minimisation; robust optimal guaranteed cost control
Subjects: Algebra; Control system analysis and synthesis methods; Stability in control theory; Distributed parameter control systems; Discrete control systems; Optimal control