Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 360928, 16 pages
Research Article

Delay-Dependent Guaranteed Cost H Control of an Interval System with Interval Time-Varying Delay

College of Automation, Northwestern Polytechnical University, Xi'an 710072, China

Received 25 January 2009; Revised 30 June 2009; Accepted 16 August 2009

Academic Editor: Alexander I. Domoshnitsky

Copyright © 2009 Min Xiao and Zhongke Shi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper concerns the problem of the delay-dependent robust stability and guaranteed cost H control for an interval system with time-varying delay. The interval system with matrix factorization is provided and leads to less conservative conclusions than solving a square root. The time-varying delay is assumed to belong to an interval and the derivative of the interval time-varying delay is not a restriction, which allows a fast time-varying delay; also its applicability is broad. Based on the Lyapunov-Ktasovskii approach, a delay-dependent criterion for the existence of a state feedback controller, which guarantees the closed-loop system stability, the upper bound of cost function, and disturbance attenuation lever for all admissible uncertainties as well as out perturbation, is proposed in terms of linear matrix inequalities (LMIs). The criterion is derived by free weighting matrices that can reduce the conservatism. The effectiveness has been verified in a number example and the compute results are presented to validate the proposed design method.