# Local Lyapunov Functions for Nonlinear Stochastic Differential Equations by Linearization

### Hjörtur Björnsson, Peter Giesl, Skuli Gudmundsson, Sigurdur Hafstein

#### Abstract

We present a rigid estimate of the domain, on which a Lyapunov function for the linearization of a nonlinear stochastic differential equation is a Lyapunov function for the original system. By using this estimate the demanding task of computing a lower bound on the γ-basin of attraction for a nonlinear stochastic systems is greatly simplified and the application of a resent numerical method for the same purpose facilitated.

Download#### Paper Citation

#### in Harvard Style

Björnsson H., Giesl P., Gudmundsson S. and Hafstein S. (2018). **Local Lyapunov Functions for Nonlinear Stochastic Differential Equations by Linearization**.In *Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 1: CTDE,* ISBN 978-989-758-321-6, pages 579-586. DOI: 10.5220/0006944505790586

#### in Bibtex Style

@conference{ctde18,

author={Hjörtur Björnsson and Peter Giesl and Skuli Gudmundsson and Sigurdur Hafstein},

title={Local Lyapunov Functions for Nonlinear Stochastic Differential Equations by Linearization},

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

year={2018},

pages={579-586},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006944505790586},

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 - Local Lyapunov Functions for Nonlinear Stochastic Differential Equations by Linearization

SN - 978-989-758-321-6

AU - Björnsson H.

AU - Giesl P.

AU - Gudmundsson S.

AU - Hafstein S.

PY - 2018

SP - 579

EP - 586

DO - 10.5220/0006944505790586