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Construction of a finite-time Lyapunov function by meshless collocation

journal contribution
posted on 2023-06-08, 21:10 authored by Peter GieslPeter Giesl
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.

History

Publication status

  • Published

Journal

Discrete and Continuous Dynamical Systems - Series B

ISSN

1531-3492

Publisher

American Institute of Mathematical Sciences

Issue

7

Volume

17

Page range

2387-2412

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2015-06-16

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