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Exact asymptotic stability analysis and region-of-attraction estimation for nonlinear systems. (English) Zbl 1271.93128

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.

MSC:

93D20 Asymptotic stability in control theory
93D30 Lyapunov and storage functions
93B40 Computational methods in systems theory (MSC2010)
37N35 Dynamical systems in control
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