On exponential stability of hybrid neutral stochastic differential delay equations with different structures

Wu, Aiqing and You, Surong and Mao, Wei and Mao, Xuerong and Hu, Liangjian (2021) On exponential stability of hybrid neutral stochastic differential delay equations with different structures. Nonlinear Analysis: Hybrid Systems, 39. 100971. ISSN 1751-570X (https://doi.org/10.1016/j.nahs.2020.100971)

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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.

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