A Class Of Hybrid Delay Systems And Applications

This article mainly focuses on a class of hybrid delay systems,studying stability,mean exit time,and parameter estimations problems.First of all,based on the LaSalle principle,we consider a class of hybrid stochastic delay differential equations driven by α-stable processes,giving sufficient conditions for the global asymptotic stability of the zero solution of the equation in terms of probability.Using the Lyapunov method,we disclose the impact on conditions for pth moment stability of hybird systems with a delay as a tends to 2,and relative theorems are proved.In the second chapter,according to the infinitesimal generator of the Markov process,we solve the Poisson equations under different boundary conditions,the explicit expressions of the mean exit time of two types of hybrid systems without delay are given,and it is proved that the mean exit time of a class of hybrid systems with delay is finite.Besides,based on the EM algorithm,some expressions for the parameter estimations of hybrid time-delay OU processes are given.