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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 737949, 11 pages
http://dx.doi.org/10.1155/2015/737949
Research Article

Exponential Stabilization of a Class of Time-Varying Delay Systems with Nonlinear Perturbations

1School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China
2Qingdao Technological University, Feixian, Shandong 273400, China
3School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China

Received 3 April 2015; Accepted 25 June 2015

Academic Editor: Xinguang Zhang

Copyright © 2015 Yazhou Tian et al. 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.

Abstract

This paper addresses the problem of exponential stabilization of a class of time-varying delay systems with nonlinear perturbations. These perturbations are related not only with current state and the delayed state but also with , where is a continuous function defined on . With the delay interval divided into two equidistant subintervals, a novel Lyapunov functional is introduced, and several new exponential stabilization criteria are derived in terms of linear matrix inequalities (LMIs) by employing reciprocally convex approach. Two examples are given to illustrate the effectiveness of the main results.