Construction of a finite-time Lyapunov function by meshless collocation

We consider a nonautonomous ordinary differential equation of the form x ? = f(t,x), x ? Rn over a finite-time interval t ? [T1,T2]. The domain of attraction of an attracting solution can be determined using a finite-time Lya- punov function. In this paper, such a finite-time Lyapunov function is constructed by Mesh- less Collocation, in particular Radial Basis Functions. Thereto, a finite-time Lyapunov function is characterised as the solution of a second-order linear par- tial differential equation with boundary values. This problem is approximately solved using Meshless Collocation, and it is shown that the approximate solu- tion can be used to determine the domain of attraction.