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Journal of Applied Mathematics
Volume 2013, Article ID 859578, 5 pages
http://dx.doi.org/10.1155/2013/859578
Research Article

Constructing the Lyapunov Function through Solving Positive Dimensional Polynomial System

1Laboratory of Computer Reasoning and Trustworthy Computation, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
2Laboratory of Automated Reasoning and Cognition, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Science, Chongqing 401120, China
3L.A.S Department of ChengDu College, University of Electronic Science and Technology of China, Chengdu 611731, China

Received 24 July 2013; Accepted 21 November 2013

Academic Editor: Bo-Qing Dong

Copyright © 2013 Zhenyi Ji 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

We propose an approach for constructing Lyapunov function in quadratic form of a differential system. First, positive polynomial system is obtained via the local property of the Lyapunov function as well as its derivative. Then, the positive polynomial system is converted into an equation system by adding some variables. Finally, numerical technique is applied to solve the equation system. Some experiments show the efficiency of our new algorithm.