Non-fragile controller design for discrete descriptor systems》.pdfVIP

ARTICLE IN PRESS Journal of the Franklin Institute 346 (2009) 914–922 /locate/jfranklin Non-fragile controller design for discrete descriptor systems a b b b, Songlin Wo , Yun Zou , Qingwei Chen , Shengyuan Xu aSchool of Electrical and Information Engineering, Jiangsu Teachers University of Technology, Changzhou 213001, PR China bSchool of Automation, Nanjing University of Science and Technology, Nanjing, 210094, PR China Received 9 November 2008; received in revised form 11 April 2009; accepted 21 July 2009 Abstract This paper is concerned with the design problem of non-fragile controller for discrete descriptor systems. The controller gain variations are assumed to be time-invariant and norm-bounded appearing in the controller coefficients. Sufficient conditions for the existence of a static state feedback controller with additive uncertainty and multiplicative uncertainty are obtained in terms of a set of matrix inequalities, respectively. With these conditions, the problems of non-fragile control for discrete descriptor systems are solved. Explicit expressions of desired non-fragile state feedback controllers are also given, and no matrix decomposition is required. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach. r 2009 Published by Elsevier Ltd. on behalf of The Franklin Institute. Keywords: Discrete descriptor systems; Non-fragile control; Controller gain variation 1. Introduction It is well known that descriptor systems (also known as singular systems, implicit