Abstract and Applied Analysis

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

Min Wu, Zhengfeng Yang, and Wang Lin

Full-text: Open access

Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 146137, 10 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511828

Digital Object Identifier
doi:10.1155/2013/146137

Mathematical Reviews number (MathSciNet)
MR3039177

Zentralblatt MATH identifier
1271.93128

Citation

Wu, Min; Yang, Zhengfeng; Lin, Wang. Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems. Abstr. Appl. Anal. 2013 (2013), Article ID 146137, 10 pages. doi:10.1155/2013/146137. https://projecteuclid.org/euclid.aaa/1393511828


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