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

Hafstein, Sigurdur, Gudmundsson, Skuli, Giesl, Peter and Scalas, Enrico (2018) Lyapunov function computation for autonomous linear stochastic differential equations using sum-of-squares programming. Discrete and Continuous Dynamical Systems - Series B, 23 (2). pp. 939-956. ISSN 1531-3492

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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: 18 Jan 2018 15:34
URI: http://sro.sussex.ac.uk/id/eprint/69942

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