Exponential stability analysis of impulsive stochastic functional differential systems with delayed impulses

Delayed impulsive synchronization of discrete-time complex networks with distributed delays

“…(4), we can see that the synchronization of discrete-time complex networks under delayed impulsive control is transformed into the stabilization problem of discrete-time systems with delayed impulses. Recently, delayed impulsive effects have considered in stability and synchronization problems of various impulsive continuous-time systems [2][3][4]34,40]. It should be mentioned that a delayed impulsive control strategy has been proposed to guarantee the synchronization of continuous-time complex networks in [40], which can generalize several impulsive control strategies, e.g., [2,8,35,36].…”

“…Therefore, it is of great importance to take into account impulsive input delays when using impulsive control strategy. Recently, impulsive input delays have been considered in continuous-time impulsive systems [3,4,34]. Based on these results, delayed impulsive control strategies, which are more general than the general impulsive control, have been proposed in [2,40].…”

Stability of impulsive delayed linear differential systems with delayed impulses

“…In [25], Khadra et al used exponential estimates to investigate the asymptotic stability for delay-free autonomous impulsive control systems with delayed impulses. Making use of Lyapunov function method combined with Razumikhin technique, Chen et al [17][18][19]29,30] studied the exponential stability for the time-delay nonlinear impulsive differential systems, nonlinear singularly perturbed systems and Takagi-Sugeno fuzzy systems with delayed impulses. Although several results of impulsive delayed systems with delayed impulses have been obtained in [17][18][19][24][25][26][27][28][29][30], some restrictions must be illustrated to get these results.…”

“…Lyapunov-Razumikhin method is one of the most useful ways in dealing with the stability of impulsive delayed differential systems, see [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] and the references cited therein. Recently, making use of Lyapunov functional and analysis technique, the stability issue has been studied in [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][32][33][34] for some impulsive control systems with time delay.…”

“…Recently, making use of Lyapunov functional and analysis technique, the stability issue has been studied in [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][32][33][34] for some impulsive control systems with time delay. Several criteria on uniformly stability, uniformly asymptotic stability and exponential stability were established, and those results show that a system can be stabilized by impulses even if it contains an unstable system matrix.…”