Stability Analysis and Region-of-Attraction Estimation Using Piecewise Polynomial Lyapunov Functions: Polynomial Fuzzy Model Approach

2015 ◽  
Vol 23 (4) ◽  
pp. 1314-1322 ◽  
Author(s):  
Ying-Jen Chen ◽  
Motoyasu Tanaka ◽  
Kazuo Tanaka ◽  
Hua O. Wang
Keyword(s):  
Stability Analysis ◽  
Lyapunov Functions ◽  
Fuzzy Model ◽  
Piecewise Polynomial ◽  
Region Of Attraction ◽  
Model Approach

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

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Min Wu ◽  
Zhengfeng Yang ◽  
Wang Lin
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Lyapunov Functions ◽  
Nonlinear Dynamical Systems ◽  
Region Of Attraction ◽  
Nonlinear Dynamical ◽  
Recovery Techniques ◽  
Regions Of Attraction

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.

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