Global exponential stability of impulsive stochastic functional differential systems

Exponential stability of impulsive stochastic functional differential equations

“…Moreover, some useful corollaries of exponential stability are derived by means of Lyapunov function, inequality techniques and the impulsive condition. The obtained results do not need the strong condition of impulsive gain |d k | < 1 as in [19]. In this sense, our results are more general than those given in [19].…”

“…The obtained results do not need the strong condition of impulsive gain |d k | < 1 as in [19]. In this sense, our results are more general than those given in [19]. Meanwhile, an example is provided to show the impulsive effects play an important role in the stability for stochastic functional differential equations in our results.…”

“…Peng and Jia [18] obtained some criteria on pth moment stability and pth moment asymptotical stability of impulsive stochastic functional differential equations by using Lyapunov-Razumikhin method. In [19], several criteria on the global exponential stability and instability of impulsive stochastic functional differential systems are obtained by Cheng and Deng. In addition, some other investigation on stability criteria of impulsive stochastic differential equation, we can find in [21,25].…”

Exponential stability of stochastic functional differential equations with Markovian switching and delayed impulses via Razumikhin method

“…So the theory of impulsive differential equations is also attracting much attention in recent years [13][14][15][16][17][18][19]. Correspondingly, a lot of stability results of impulsive stochastic functional differential equations have been obtained [20][21][22][23][24][25][26]. However, there are few results on the stability of impulsive stochastic differential equation with Markovian switching.…”

“…The state variables on the impulses relate to the finite delay, which implies that the impulsive effects are more general than those given in [20,22,23]. Some Theorems on the pth moment exponential stability are derived in the case that the impulsive gain d ik +d ik < 1 or d ik +d ik ≥ 1.…”