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Abstract and Applied Analysis
Volume 2013, Article ID 146137, 10 pages
Research Article

Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems

1Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China
2College of Mathematics and Information Science, Wenzhou University, Wenzhou Zhejiang 325035, China

Received 14 November 2012; Revised 11 February 2013; Accepted 20 February 2013

Academic Editor: Fabio M. Camilli

Copyright © 2013 Min Wu 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.


We address the problem of asymptotic stability and region-of-attraction analysis of nonlinear dynamical systems. A hybrid symbolic-numeric method is presented to compute exact Lyapunov functions and exact estimates of regions of attraction of nonlinear systems efficiently. A numerical Lyapunov function and an estimate of region of attraction can be obtained by solving an (bilinear) SOS programming via BMI solver, then the modified Newton refinement and rational vector recovery techniques are applied to obtain exact Lyapunov functions and verified estimates of regions of attraction with rational coefficients. Experiments on some benchmarks are given to illustrate the efficiency of our algorithm.