Almost sure exponential stability of stochastic differential delay equations
Guo, Qian and Mao, Xuerong and Yue, Rongxian (2016) Almost sure exponential stability of stochastic differential delay equations. SIAM Journal on Control and Optimization, 54 (4). pp. 1919-1933. ISSN 0363-0129 (https://doi.org/10.1137/15M1019465)
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Abstract
This paper is concerned with the almost sure exponential stability of the multidimensional nonlinear stochastic differential delay equation (SDDE) with variable delays of the form dx(t) = f(x(t−δ1(t)), t)dt+g(x(t−δ2(t)), t)dB(t), where δ1, δ2 : R+ → [0, τ ] stand for variable delays. We show that if the corresponding (nondelay) stochastic differential equation (SDE) dy(t) = f(y(t), t)dt + g(y(t), t)dB(t) admits a Lyapunov function (which in particular implies the almost sure exponential stability of the SDE) then there exists a positive number τ ∗ such that the SDDE is also almost sure exponentially stable as long as the delay is bounded by τ ∗ . We provide an implicit lower bound for τ ∗ which can be computed numerically. Moreover, our new theory enables us to design stochastic delay feedback controls in order to stabilize unstable differential equations
ORCID iDs
Guo, Qian, Mao, Xuerong ORCID: https://orcid.org/0000-0002-6768-9864 and Yue, Rongxian;-
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Item type: Article ID code: 56581 Dates: DateEvent27 July 2016Published1 June 2016AcceptedSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 02 Jun 2016 10:34 Last modified: 21 Sep 2024 00:37 URI: https://strathprints.strath.ac.uk/id/eprint/56581