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Received Apr 12, 2017; Revised Jul 2, 2017; Accepted Jul 19, 2017
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1. Introduction
With the deep development of the research on complex systems in recent years, much attention has been paid to the influence of random factors on the power system. Hence, the stochastic differential equations (SDEs) come to play important roles in many fields, such as molecular physics, population genetics, and some other branches of science (see [1–3]).
Practically, there are many systems depending on both present and past states, as well as the changing rate. To model this kind of systems primely, the delay systems and neutral stochastic differential equations (NSDEs) with time-dependent delay are studied widely. Recently, there have appeared many interesting results in the literature. For example, [4–6] studied the global asymptotic stability results and applications of time-varying delay systems in neural networks (NNs), memristive neural networks (MNNs), and chaotic Lure systems (CLSs). Zhu and Cao [7] investigated the global asymptotic stability for stochastic neural networks of neutral type with both Markovian jump parameters and mixed time delays. Liu and Zhu [8] studied mean square stability of two classes of theta method for NSDEs with bounded delay. Ma and Xi [9] established a moderate deviation principle for NSDEs driven by Poisson random measure and time delay.
On the other hand, some random abrupt changes generally exist in practical systems because of the change of internal and external environment. SDEs with Markovian switching (SDEwMs) are powerful tools for describing systems that encounter abrupt changes in structure. It is inspiring that many important results have been reported in the literature. For example, Zhu et al. [10] investigated the problem of robust exponential stability for a class of stochastically nonlinear jump systems with mixed time delays. Zhu [11] investigated the