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Estimating the domain of attraction via union of continuous families of Lyapunov estimates. (English) Zbl 1109.37012
Summary: This paper proposes a new approach to estimate the domain of attraction of equilibrium points of polynomial systems. The idea consists of estimating the domain of attraction via the union of a continuous family of Lyapunov estimates rather than via one Lyapunov estimate only as done in existing methods. This family is obtained through a convex LMI optimization by deriving a stability condition which takes simultaneously into account all Lyapunov functions considered. Moreover, inner approximations to the union of this family via a set with simple shape are derived, too.

MSC:
37B25 Stability of topological dynamical systems
90C25 Convex programming
Software:
SeDuMi; YALMIP
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