Recently, Mao [19] initiates the study the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations by feedback controls based on discrete-time state observations. Mao [19] also obtains an upper bound on the duration τ between two consecutive state observations. However, it is due to the general technique used there that the bound on τ is not very sharp. In this paper, we will be able to establish a better bound on τ making use of Lyapunov functionals. We will not only discuss the stabilization in the sense of exponential stability (as Mao [19] does) but also in other sense of H ∞ stability or asymptotic stability. We will not only consider the mean square stability but also the almost sure stability.

Feedback control based on discrete-time state observation for stochastic differential equations with Markovian switching was initialled by Mao (2013). In practice, various effects could cause some time delay in the control function. Therefore, the time delay is taken into account for the discrete-time state observation in this paper and the mean-square exponential stability of the controlled system IS investigated.This paper is devoted as a continuous research to Mao (2013).

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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.