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

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