Local Lyapunov functions for nonlinear stochastic differential equations by linearization

Hjörtur Björnsson; Peter Giesl; Skuli Gudmundsson; Sigurdur Hafstein

doi:10.5220/0006944505790586

Local Lyapunov functions for nonlinear stochastic differential equations by linearization

Hjörtur Björnsson, Peter Giesl, Skuli Gudmundsson, Sigurdur Hafstein

Faculty of Physical Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Citations (Scopus)

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.

Original language	English
Title of host publication	ICINCO 2018 - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics
Editors	Kurosh Madani, Oleg Gusikhin
Publisher	SciTePress
Pages	579-586
Number of pages	8
ISBN (Electronic)	9789897583216
DOIs	https://doi.org/10.5220/0006944505790586
Publication status	Published - 2018
Event	15th International Conference on Informatics in Control, Automation and Robotics, ICINCO 2018 - Porto, Portugal Duration: 29 Jul 2018 → 31 Jul 2018

Publication series

Name	ICINCO 2018 - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics
Volume	1

Conference

Conference	15th International Conference on Informatics in Control, Automation and Robotics, ICINCO 2018
Country/Territory	Portugal
City	Porto
Period	29/07/18 → 31/07/18

Bibliographical note

Publisher Copyright:
Copyright © 2018 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

Other keywords

Asymptotic Stability in Probability
Linearization
Lyapunov Function
Stochastic Differential Equation

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10.5220/0006944505790586

Cite this

Björnsson, H., Giesl, P., Gudmundsson, S., & Hafstein, S. (2018). Local Lyapunov functions for nonlinear stochastic differential equations by linearization. In K. Madani, & O. Gusikhin (Eds.), ICINCO 2018 - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics (pp. 579-586). (ICINCO 2018 - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics; Vol. 1). SciTePress. https://doi.org/10.5220/0006944505790586

Björnsson, Hjörtur ; Giesl, Peter ; Gudmundsson, Skuli et al. / Local Lyapunov functions for nonlinear stochastic differential equations by linearization. ICINCO 2018 - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics. editor / Kurosh Madani ; Oleg Gusikhin. SciTePress, 2018. pp. 579-586 (ICINCO 2018 - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics).

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title = "Local Lyapunov functions for nonlinear stochastic differential equations by linearization",

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.",

keywords = "Asymptotic Stability in Probability, Linearization, Lyapunov Function, Stochastic Differential Equation",

author = "Hj{\"o}rtur Bj{\"o}rnsson and Peter Giesl and Skuli Gudmundsson and Sigurdur Hafstein",

note = "Publisher Copyright: Copyright {\textcopyright} 2018 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved; 15th International Conference on Informatics in Control, Automation and Robotics, ICINCO 2018 ; Conference date: 29-07-2018 Through 31-07-2018",

year = "2018",

doi = "10.5220/0006944505790586",

language = "English",

series = "ICINCO 2018 - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics",

publisher = "SciTePress",

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booktitle = "ICINCO 2018 - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics",

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Björnsson, H, Giesl, P, Gudmundsson, S & Hafstein, S 2018, Local Lyapunov functions for nonlinear stochastic differential equations by linearization. in K Madani & O Gusikhin (eds), ICINCO 2018 - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics. ICINCO 2018 - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics, vol. 1, SciTePress, pp. 579-586, 15th International Conference on Informatics in Control, Automation and Robotics, ICINCO 2018, Porto, Portugal, 29/07/18. https://doi.org/10.5220/0006944505790586

Local Lyapunov functions for nonlinear stochastic differential equations by linearization. / Björnsson, Hjörtur; Giesl, Peter; Gudmundsson, Skuli et al.

ICINCO 2018 - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics. ed. / Kurosh Madani; Oleg Gusikhin. SciTePress, 2018. p. 579-586 (ICINCO 2018 - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics; Vol. 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Local Lyapunov functions for nonlinear stochastic differential equations by linearization

AU - Björnsson, Hjörtur

AU - Giesl, Peter

AU - Gudmundsson, Skuli

AU - Hafstein, Sigurdur

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Asymptotic Stability in Probability

KW - Linearization

KW - Lyapunov Function

KW - Stochastic Differential Equation

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DO - 10.5220/0006944505790586

M3 - Conference contribution

AN - SCOPUS:85071542642

T3 - ICINCO 2018 - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics

SP - 579

EP - 586

BT - ICINCO 2018 - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics

A2 - Madani, Kurosh

A2 - Gusikhin, Oleg

PB - SciTePress

T2 - 15th International Conference on Informatics in Control, Automation and Robotics, ICINCO 2018

Y2 - 29 July 2018 through 31 July 2018

ER -

Björnsson H, Giesl P, Gudmundsson S, Hafstein S. Local Lyapunov functions for nonlinear stochastic differential equations by linearization. In Madani K, Gusikhin O, editors, ICINCO 2018 - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics. SciTePress. 2018. p. 579-586. (ICINCO 2018 - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics). doi: 10.5220/0006944505790586

Local Lyapunov functions for nonlinear stochastic differential equations by linearization

Abstract

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