The Stability For A Class Of Stochastic Hybrid Systems

Stochastic hybrid system is one piece of hybrid systems which are defined on hybrid states space,with both continuous and discrete states.Ones can get many stochastic hybrid systems from the differences of the states changing.The paper studies one of Stochastic hybrid system,which transitions occur with the probability one when its continuous state hits the boundary of the state space,whenever a transition occurs the hybrid state is reset instantly to a new value.The value of the discrete state after the transition is determined by the hybrid state before the transition,the valuc of continuous state is governed by a probability law depending last hybrid state,which obeys stochastic differential equations whose solution is a stochastic process.This paper discusses the stability and asymptotic stability with the extended It(?) differential rule,a Sufficient condition is given to caprice the systems stable.Furthermore,the LaSalle invariance priciple is consider for such systems.