Abstract
AbstractThis 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 ε‐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 ε‐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 ε 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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