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

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 funct...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2013-01, Vol.2013 (2013), p.661-670
Main Authors: Wu, Min, Lin, Wang, Yang, Zhengfeng
Format: Article
Language:English
Subjects:
Dynamical systems
Liapunov functions
Linear programming
Mathematical research
Nonlinear theories
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Summary: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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/146137