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.

Recently, Mao (2013) discusses the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations by feedback controls based on discrete-time state observations. Mao (2013) 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 consider a couple of important classes of hybrid SDEs. Making full use of their special features, we will be able to establish a better bound on τ . Our new theory enables us to observe the system state less frequently (so costs less) but still to be able to design the feedback control based on the discrete-time state observations to stabilize the given hybrid SDEs in the sense of mean-square exponential stability

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Recently, a kind of feedback control based on discrete-time state observations was proposed to stabilize continuous-time hybrid stochastic systems in the mean-square sense. We find that the feedback control there still depends on the continuous-time observations of the mode. However, it usually costs to identify the current mode of the system in practice. So we can further improve the control to reduce the control cost by identifying the mode at discrete times when we make observations for the state. In this paper, we aim to design such a type of feedback control based on the discrete-time observations of both state and mode to stabilize the given hybrid stochastic differential equations (SDEs) in the sense of mean-square exponential stability. Moreover, a numerical example is given to illustrate our results.

This paper mainly investigates stabilization of hybrid stochastic differential equations (SDEs) via periodically intermittent feedback controls based on discrete-time state observations with a time delay. First, by using the theory of M-matrix and intermittent control strategy, we establish sufficient conditions for the stability of hybrid SDEs. Then, we prove the intermittent stabilization for a given unstable nonlinear hybrid SDE by comparison theorem. Two numerical examples are discussed to support our results of theoretical analysis.