Lyapunov function computation for autonomous linear stochastic differential equations using sum-of-squares programming

Hafstein, Sigurdur, Gudmundsson, Skuli, Giesl, Peter and Scalas, Enrico (2017) Lyapunov function computation for autonomous linear stochastic differential equations using sum-of-squares programming. Discrete and Continuous Dynamical Systems - Series B, 22. ISSN 1531-3492 (Accepted)

[img] PDF - Accepted Version
Restricted to SRO admin only

Download (476kB)

Abstract

We study the global asymptotic stability in probability of the zero solution of linear stochastic differential equations with constant coefficients. We develop a sum-of-squares program that verifies whether a parameterized candidate Lyapunov function is in fact a global Lyapunov function for such a system. Our class of candidate Lyapunov functions are naturally adapted to the problem. We consider functions of the form V(x) = ||x||pQ := (xt>Qx) p/2, where the parameters are the positive definite matrix Q and the number p > 0. We give several examples of our proposed method and show how it improves previous results.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Analysis and Partial Differential Equations Research Group
Subjects: Q Science > QA Mathematics
Related URLs:
Depositing User: Billy Wichaidit
Date Deposited: 31 Aug 2017 10:55
Last Modified: 31 Aug 2017 11:01
URI: http://sro.sussex.ac.uk/id/eprint/69942

View download statistics for this item

📧 Request an update