Local Lyapunov Functions for Nonlinear Stochastic Differential Equations by Linearization

Hjörtur Björnsson; Peter Giesl; Skuli Gudmundsson; Sigurdur Hafstein

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Paper

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, 579-586, 2018 , Porto, Portugal

Authors: Hjörtur Björnsson ¹ ; Peter Giesl ² ; Skuli Gudmundsson ³ and Sigurdur Hafstein ¹

Affiliations: ¹ Science Institute and Faculty of Physical Sciences, University of Iceland, Dunhagi 5, 107 Reykjavík and Iceland ; ² Department of Mathematics, University of Sussex, Falmer, BN1 9QH and U.K. ; ³ Svensk Exportkredit, Klarabergsviadukten 61-63, 11164 Stockholm and Sweden

Keyword(s): Stochastic Differential Equation, Lyapunov Function, Linearization, Asymptotic Stability in Probability.

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.

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Paper citation in several formats:

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; ISSN 2184-2809, SciTePress, pages 579-586. DOI: 10.5220/0006944505790586

@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},
issn={2184-2809},
}

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
IS - 2184-2809
AU - Björnsson, H.
AU - Giesl, P.
AU - Gudmundsson, S.
AU - Hafstein, S.
PY - 2018
SP - 579
EP - 586
DO - 10.5220/0006944505790586
PB - SciTePress