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Mathematical Problems in Engineering
Volume 2015, Article ID 425864, 9 pages
Research Article

New Stability Analysis for Linear Systems with Time-Varying Delay Based on Combined Convex Technique

The School of Control Science and Engineering, Dalian University of Technology, Dalian 116023, China

Received 8 March 2014; Accepted 5 August 2014

Academic Editor: Huaguang Zhang

Copyright © 2015 Bin Yang and Chen-xin Fan. 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.


A novel combined convex method is developed for the stability of linear systems with a time-varying delay. A new delay-dependent stability condition expressed in terms of linear matrix inequalities (LMIs) is derived by employing a dedicated constructed Lyapunov-Krasovskii functional (LKF), utilizing the Wirtinger inequality and the reciprocally convex approach to handle the integral term of quadratic quantities. Different from the previous convex techniques which only tackle the time-varying delay, our method adopts the idea of combined convex technique which can tackle not only the delay but also the delay variation. Four well-known examples are illustrated to show the effectiveness of the proposed results.