# Combination of Refinement and Verification for the Construction of Lyapunov Functions using Radial Basis Functions

### Peter Giesl, Najla Mohammed

#### Abstract

Lyapunov functions are an important tool for the determination of the domain of attraction of an equilibrium point of a given ordinary differential equation. The Radial Basis Functions collocation method is one of the numerical methods to construct Lyapunov functions. This method has been improved by combining it with a refinement algorithm to reduce the number of collocation points required in the construction process, as well as a verification that the constructed function is a Lyapunov function. In this paper, we propose a combination of both methods in one, called the combination method. This method constructs a Lyapunov function with the refinement algorithm and then verifies its properties rigorously. The method is illustrated with examples.

Download#### Paper Citation

#### in Harvard Style

Giesl P. and Mohammed N. (2018). **Combination of Refinement and Verification for the Construction of Lyapunov Functions using Radial Basis Functions**.In *Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 1: CTDE,* ISBN 978-989-758-321-6, pages 569-578. DOI: 10.5220/0006944405690578

#### in Bibtex Style

@conference{ctde18,

author={Peter Giesl and Najla Mohammed},

title={Combination of Refinement and Verification for the Construction of Lyapunov Functions using Radial Basis Functions},

booktitle={Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 1: CTDE,},

year={2018},

pages={569-578},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006944405690578},

isbn={978-989-758-321-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 1: CTDE,

TI - Combination of Refinement and Verification for the Construction of Lyapunov Functions using Radial Basis Functions

SN - 978-989-758-321-6

AU - Giesl P.

AU - Mohammed N.

PY - 2018

SP - 569

EP - 578

DO - 10.5220/0006944405690578