Lyapunov functions for linear stochastic differential equations: BMI formulation of the conditions

Sigurdur Hafstein*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We present a bilinear matrix inequality (BMI) formulation of the conditions for a Lyapunov functions for autonomous, linear stochastic differential equations (SDEs). We review and collect useful results from the theory of stochastic stability of the null solution of an SDE. Further, we discuss the Itô- and Stratonovich interpretation and linearizations and Lyapunov functions for linear SDEs. Then we discuss the construction of Lyapunov functions for the damped pendulum, wihere the spring constant is modelled as a stochastic process. We implement in Matlab the characterization of its canonical Lyapunov function as BMI constraints and consider some practical implementation strategies. Further, we demonstrate that the general strategy is applicable to general autonomous and linear SDEs. Finally, we verify our findings by comparing with results from the literature.

Original languageEnglish
Title of host publicationICINCO 2019 - Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics
EditorsOleg Gusikhin, Kurosh Madani, Janan Zaytoon
PublisherSciTePress
Pages147-155
Number of pages9
ISBN (Electronic)9789897583803
DOIs
Publication statusPublished - 2019
Event16th International Conference on Informatics in Control, Automation and Robotics, ICINCO 2019 - Prague, Czech Republic
Duration: 29 Jul 201931 Jul 2019

Publication series

NameICINCO 2019 - Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics
Volume1

Conference

Conference16th International Conference on Informatics in Control, Automation and Robotics, ICINCO 2019
Country/TerritoryCzech Republic
CityPrague
Period29/07/1931/07/19

Bibliographical note

Publisher Copyright:
Copyright © 2019 by SCITEPRESS - Science and Technology Publications, Lda. All rights reserved.

Other keywords

  • Bilinear matrix inequalities
  • Lyapunov function
  • Stochastic differential equation

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