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

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posted on 2023-06-09, 07:43 authored by Sigurdur Hafstein, Skuli Gudmundsson, Peter GieslPeter Giesl, Enrico Scalas
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.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Discrete and Continuous Dynamical Systems - Series B

ISSN

1531-3492

Publisher

American Institute of Mathematical Sciences

Issue

2

Volume

23

Page range

939-956

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Analysis and Partial Differential Equations Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2017-08-31

First Open Access (FOA) Date

2019-01-01

First Compliant Deposit (FCD) Date

2017-08-31

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