Construction of a finite-time Lyapunov function by meshless collocation

Giesl, Peter (2012) Construction of a finite-time Lyapunov function by meshless collocation. Discrete and Continuous Dynamical Systems - Series B, 17 (7). pp. 2387-2412. ISSN 1531-3492

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Abstract

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.

Item Type: Article
Keywords: Nonautonomous Ordinary Differential Equation, Finite-time Lya- punov Function, Domain of Attraction, Meshless Collocation, Radial Basis Func- tions, Error Estimates.
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Peter Giesl
Date Deposited: 16 Jun 2015 16:53
Last Modified: 16 Jun 2015 16:53
URI: http://sro.sussex.ac.uk/id/eprint/54586
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