A NEW RESULT ON STATE FEEDBACK ROBUST STABILIZATION FOR DISCRETE-TIME FUZZY SINGULARLY PERTURBED SYSTEMS

This paper presents the novel results for stabilizing uncertain standard discrete-time fuzzy singularly perturbed systems (SPSs) via a state feedback control law. Two standard discrete-time fuzzy SPSs are constructed firstly by using the Takagi-Sugeno (T-S) fuzzy model. Based on a matrix spectral norm approach, two new e-dependent stability conditions are derived, which guarantee the resulting closed-loop systems are asymptotically stable. The gains of controllers are obtained by solving a set of e-dependent linear matrix inequalities (LMIs). In contrast to the existing results, the proposed methods have two advantages: (i) the designed controllers can overcome the external disturbances and parameter uncertainty; and (ii) the upper bound of e is improved, especially it is not required to be smaller than one. Examples are provided to illustrate the reduced conservatism of our results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

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