Abstract This article discusses the problem of exponential stability for a class of hybrid neutral stochastic differential delay equations with highly nonlinear coefficients and different structures in different switching modes. In such systems, the coefficients will satisfy the local Lipschitz condition and suitable Khasminskii-types conditions. The set of switching states will be divided into two subsets. In different subsets, the coefficients will be dominated by polynomials with different degrees. By virtue of M -matrices and suitable Lyapunov functions dependent on coefficient structures and switching modes, some results including the existence-and-uniqueness, boundedness and exponential stability of the solution are proposed and proved.

中文翻译：

---

不同结构混合中性随机微分时滞方程的指数稳定性

摘要 本文讨论了一类具有高度非线性系数和不同开关模式下不同结构的混合中性随机微分时滞方程的指数稳定性问题。在这样的系统中，系数将满足局部 Lipschitz 条件和合适的 Khasminskii 类型条件。这组开关状态将分为两个子集。在不同的子集中，系数会以不同次数的多项式为主。利用M矩阵和依赖于系数结构和切换模式的合适的Lyapunov函数，提出并证明了解的存在唯一性、有界性和指数稳定性等一些结果。