Stabilization Of Stochastic Switching Processes By Feedback Control Based On Discrete-time State Observations

Recently,Cao et al(2019)had constructed the Lyapunov function to study the asymptotic stability of stochastic switching differential equations driven by linear discrete time noises,but which they studied did not take into account poisson jump processes.In this paper,we study the pth moment exponential stability of stochastic differential equations by feedback control based on the noises of the discrete-time observations.For stochastic differential equations with state-dependent switching,the existence and u-niqueness of its solution are studied by using the conclusions of Pei&Xu in 2017,whose coefficients satisfy the non-lipschitz conditions,then,the sufficient conditions for its pth mo-ment exponential stability are received by combining M Matrix with the relations of the state-dependent switching process and the homogeneous Markov process given by Xi&Gin in 2013,finally,the criteria of its pth moment exponential stability are obtained by the results of Shao&Xi in 2019 and some examples are presented to verify these results.For stochastic differential equations with Markov switching,its pth moment exponential stability is studied by constructing auxiliary equations with help of Zhao&Zhang's ideas in 2017,which satisfy the pth moment exponential stability,then,its asymptotic Boundedness in mean square is studied by improving the vector Lyapunov function given by Liu in 2016,finally,the sufficient conditions of its exponential stability in mean square are obtained by the Vector Lyapunov functions and the Multiple Lyapunov function given by Wu&Liu in 2017 and some examples are presented to verify these results.