@inproceedings{4bc6b193c4d44222ad012f517067461e,
title = "Lyapunov functions for linear stochastic differential equations: BMI formulation of the conditions",
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 It{\^o}- 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.",
keywords = "Bilinear matrix inequalities, Lyapunov function, Stochastic differential equation",
author = "Sigurdur Hafstein",
note = "Publisher Copyright: Copyright {\textcopyright} 2019 by SCITEPRESS - Science and Technology Publications, Lda. All rights reserved.; 16th International Conference on Informatics in Control, Automation and Robotics, ICINCO 2019 ; Conference date: 29-07-2019 Through 31-07-2019",
year = "2019",
doi = "10.5220/0008192201470155",
language = "English",
series = "ICINCO 2019 - Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics",
publisher = "SciTePress",
pages = "147--155",
editor = "Oleg Gusikhin and Kurosh Madani and Janan Zaytoon",
booktitle = "ICINCO 2019 - Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics",
}