Brief paper: Robustness of exponential stability of a class of stochastic functional differential equations with infinite delay

Authors:
Yangzi Hu;Fuke Wu;Chengming Huang
Affiliations:
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, PR China;School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, PR China;School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, PR China
Venue:
Automatica (Journal of IFAC)
Year:
2009

Citing 7
Cited 3

Robustness of stability of nonlinear systems with stochastic delay perturbations

Systems & Control Letters
Exact and discretized stability of the pantograph equation

Selected papers of the second international conference on Numerical solution of Volterra and delay equations : Volterra centennial: Volterra centennial
Stabilization of a class of nonlinear stochastic systems

Nonlinear Analysis: Theory, Methods & Applications
Absolutely exponential stability of a class of neural networks with unbounded delay

Neural Networks
Stabilization and destabilization of hybrid systems of stochastic differential equations

Automatica (Journal of IFAC)
Brief paper: Almost sure exponential stabilisation of stochastic systems by state-feedback control

Automatica (Journal of IFAC)
Robust stability and controllability of stochastic differential delay equations with Markovian switching

Automatica (Journal of IFAC)

Brief paper: Global stability analysis for stochastic coupled systems on networks

Automatica (Journal of IFAC)
Attraction, stability and robustness for stochastic functional differential equations with infinite delay

Automatica (Journal of IFAC)
Razumikhin-type theorems on general decay stability of stochastic functional differential equations with infinite delay

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	22.15

Visualization

Abstract

We regard the stochastic functional differential equation with infinite delay dx(t)=f(x"t)dt+g(x"t)dw(t) as the result of the effects of stochastic perturbation to the deterministic functional differential equation x@?(t)=f(x"t), where x"t=x"t(@q)@?C((-~,0];R^n) is defined by x"t(@q)=x(t+@q),@q@?(-~,0]. We assume that the deterministic system with infinite delay is exponentially stable. In this paper, we shall characterize how much the stochastic perturbation can bear such that the corresponding stochastic functional differential system still remains exponentially stable.