An algorithm for estimating attracting set of weak attractor for a class of unstable systems

There are examples of systems in which equilibria is Lyapunov-unstable, but is located on a boundary of a forward-invariant set. For initial conditions in this set corresponding solutions remains bounded and the equilibrium in some case is a weak attractor. The goal of this paper is to find an algorithm for estimating for-ward invariant set for a class of unstable systems. The proposed algorithm is based on Lemma 1 from [1] and transform original problem to optimal control or optimization problem.