The Asymptotic Properties Of Differential Systems With Impulsive Effects Suffered By Logic Choice

In this paper,the research consists of two parts,the first is studying the exponential stability of the differential systems with impulsive effects suffered by logic choice,stochastic stability and exponential stability in mean square of the stochastic differential systems with impulsive effects suffered by logic choice,and the second is studying the stochastic stability of the stochastic differential systems of impulsive effects suffered by logic choice and Markovian switching.For the differential systems with impulsive effects suffered by logic choice,we use the methods of semi-tensor product and Lyapunov function to have a discussion in the first part of this paper,under different assumptions we give the criterion for the exponential stability of the differential systems with impulsive effects suffered by logic choice,stochastic stability and exponential stability in mean square of the stochastic differential systems with impulsive effects suffered by logic choice,and finally we give a numerical simulation to illustrate our result.For the stochastic differential systems of impulsive effects suffered by logic choice and Markovian switching,we use the methods to have a study in the same way,under different assumptions we give the criterion for the stochastic stability of the stochastic differential systems of impulsive effects suffered by logic choice and Markovian switching,in addition,we give a numerical simulation to illustrate the validity of the result in the same way.