Robust guaranteed cost control for a class of two-dimensional discrete systems with shift-delays

Authors:
Shuxia Ye;Weiqun Wang;Yun Zou
Affiliations:
School of Automation, Nanjing University of Science and Technology, Nanjing, People's Republic of China 210094;Department of Mathematics, Nanjing University of Science and Technology, Nanjing, People's Republic of China 210094;School of Automation, Nanjing University of Science and Technology, Nanjing, People's Republic of China 210094
Venue:
Multidimensional Systems and Signal Processing
Year:
2009

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Abstract

This paper considers the problem of robust guaranteed cost control for uncertain two-dimensional (2-D) discrete shift-delayed systems in Fornasini---Marchesini (FM) second model. The parameter uncertainty is assumed to be norm-bounded. The problem addressed is the design of state feedback controllers such that the closed-loop system is asymptotically stable and an adequate level of performance can be guaranteed for all admissible uncertainties. The cost function with shift-delays is proposed and an upper bound of the cost function is given. In terms of a linear matrix inequality (LMI), a sufficient condition for the solvability of the problem is obtained. A desired state feedback controller can be constructed by solving a certain LMI. A numerical example is provided to demonstrate the application of the proposed method.