Region of attraction estimation using invariant sets and rational Lyapunov functions

Giorgio Valmorbida (1) , James Anderson (2)

1 L2S - Laboratoire des signaux et systèmes
2 CALTECH - California Institute of Technology

This work addresses the problem of estimating the region of attraction (RA) of equilibrium points of nonlinear dynamical systems. The estimates we provide are given by positively invariant sets which are not necessarily defined by level sets of a Lyapunov function. Moreover, we present conditions for the existence of Lyapunov functions linked to the positively invariant set formulation we propose. Connections to fundamental results on estimates of the RA are presented and support the search of Lyapunov functions of a rational nature. We then restrict our attention to systems governed by polynomial vector fields and provide an algorithm that is guaranteed to enlarge the estimate of the RA at each iteration.

Mots clés: Estimates of Region of Attraction; Polynomial systems; Invariant sets; Sum-of-squares

Domaines: Automatique / Robotique

Giorgio Valmorbida, James Anderson. Region of attraction estimation using invariant sets and rational Lyapunov functions. Automatica, 2017, 75, pp.37-45. ⟨10.1016/j.automatica.2016.09.003⟩. ⟨hal-01576290⟩