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Mathematical Problems in Engineering
Volume 2014, Article ID 301235, 8 pages
http://dx.doi.org/10.1155/2014/301235
Research Article

Stability Analysis of Fractional-Order Nonlinear Systems with Delay

Yu Wang1,2 and Tianzeng Li1,2

1School of Science, Sichuan University of Science and Engineering, Zigong 643000, China
2Sichuan Province University Key Laboratory of Bridge Non-Destruction Detecting and Engineering Computing, Sichuan University of Science and Engineering, Zigong 643000, China

Received 16 February 2014; Revised 23 March 2014; Accepted 25 March 2014; Published 16 April 2014

Academic Editor: Yuxin Zhao

Copyright © 2014 Yu Wang and Tianzeng Li. 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

Stability analysis of fractional-order nonlinear systems with delay is studied. We propose the definition of Mittag-Leffler stability of time-delay system and introduce the fractional Lyapunov direct method by using properties of Mittag-Leffler function and Laplace transform. Then some new sufficient conditions ensuring asymptotical stability of fractional-order nonlinear system with delay are proposed firstly. And the application of Riemann-Liouville fractional-order systems is extended by the fractional comparison principle and the Caputo fractional-order systems. Numerical simulations of an example demonstrate the universality and the effectiveness of the proposed method.