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Robust optimal guaranteed cost control for 2D discrete systems

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3 Author(s)
X. Guan ; Inst. of Electr. Eng., Yanshan Univ., Qinhuangdao, China ; C. Long ; G. Duan

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

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IEE Proceedings - Control Theory and Applications  (Volume:148 ,  Issue: 5 )