Abstract
In this paper, we consider a class of nonlinear stochastic systems with respect to neutral terms and time-varying delays. Given a globally exponentially stable nonlinear stochastic system, the robustness of the global exponential stability of the system subject to a time delay and a neutral term can be derived by a subtle inequality and a transcendental equation. The upper bound of the allowable time delays and the neutral terms contraction coefficient is easy to verify and implement. Finally, an example with a numerical simulation is given to illustrate the presented criteria.
Highlights
1 Introduction In the recent few decades, nonlinear stochastic systems have been widely studied by many authors due to the fact that nonlinear stochastic systems can be applied to population ecology, steam processes, heat exchanges, the distributed networks containing lossless transmission lines, and other engineering systems
One of the important issues in the study of Neutral stochastic differential delay equations (NSDDEs) is the automatic control, with consequent emphasis being placed on the analysis of stability
For a globally exponentially stable nonlinear stochastic system, if the time delay and neutral term contraction coefficient are smaller than the derived upper bounds, the perturbed nonlinear stochastic system is guaranteed to stay globally exponentially stable
Summary
In the recent few decades, nonlinear stochastic systems have been widely studied by many authors due to the fact that nonlinear stochastic systems can be applied to population ecology, steam processes, heat exchanges, the distributed networks containing lossless transmission lines, and other engineering systems. Xu et al Advances in Difference Equations (2015) 2015:105 and Wang [ ] studied the noise-induced stabilization of the recurrent neural networks with mixed time-varying delays and Markovian switching parameters. In [ – ], the authors investigated the robustness of global exponential stability of stochastic systems (with Markovian switching) in the presence of time-varying delays or noises. Shen and Wang [ ] discussed the robustness of global exponential stability of nonlinear systems in the presence of time delays and neutral terms. We will consider a class of nonlinear stochastic systems with respect to neutral terms and time-varying delays. In Section , the robustness of global exponential stability of nonlinear stochastic systems with respect to neutral terms and time-varying delays is analyzed and a corollary for our theorem is derived.
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