Robust Region-of-Attraction Estimation

We propose a method to compute invariant subsets of the region-of-attraction for asymptotically stable equilibrium points of polynomial dynamical systems with bounded parametric uncertainty. Parameter-independent Lyapunov functions are used to characterize invariant subsets of the robust region-of-attraction. A branch-and-bound type refinement procedure reduces the conservatism. We demonstrate the method on an example from the literature and uncertain controlled short-period aircraft dynamics

Region of Attraction Estimation Using Invariant Sets and Rational Lyapunov Functions

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