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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 9626725, 8 pages
http://dx.doi.org/10.1155/2016/9626725
Research Article

New Exponential Stability Results for Neutral Stochastic Systems with Distributed Delays

School of Mathematics and Statistics, Anyang Normal University, Anyang, Henan 455002, China

Received 18 April 2016; Revised 12 September 2016; Accepted 9 October 2016

Academic Editor: Mohammad D. Aliyu

Copyright © 2016 Jian Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper studies the stability problem of a grey neutral stochastic system with distributed delays. The main feature of a grey system is that the parameters of system are evaluated by grey numbers, and system has the strong background in engineering applications. However, the literature dealing with the stability problem for grey system seems to be scarce. The main aim of this paper is to fill the gap. Based on the Lyapunov stability theorem and Itô’s formula, especially, using the decomposition technique of the continuous matrix-covered sets of grey matrix, we propose several novel sufficient conditions, which ensure our considered grey system in mean-square exponential stability and almost surely exponential stability. Furthermore, two examples are provided to show the effectiveness of the obtained results.