On delay-dependent stabilization of retarded systems-an integral-inequality based approach

Abstract

In this paper, a new integral-inequality method is proposed by taking both the Leibniz-Newton formula and the discussed system into account. By using a Lyapunov-Krasovskii functional approach combined with the new integral inequality, we present the new stabilization criteria for the time-delay system which employs a memoryless state feedback control law. We exert ourselves to find a less conservative transformation way by bringing the free weighting matrices into the integral inequality, and also these free matrices express greatly the relationships among the system variables and among the terms in the Leibniz-Newton formula. The techniques applied here improve the results in existing literature. The results obtained by solving LMIs in this note are illustrated to be less conservative comparing with the previous ones. Moreover, numerical examples demonstrate the validity and the evident superiority of the proposed criteria. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society