Synchronization Analysis of Complex Dynamical Networks Subject to Delayed Impulsive Disturbances

Abstract

This paper studies the problem of leader-following synchronization for complex networks subject to delayed impulsive disturbances, where two kinds of time delays considered exist in internal complex networks and impulsive disturbances. Some delay-dependent sufficient criteria are derived in terms of linear matrix inequalities (LMIs) by using the delayed impulsive differential inequality method. Moreover, a feedback controller is designed to realize desired synchronization via the established LMIs. Our proposed results show that the requirements of impulse intervals and impulse sizes are dropped, and delayed impulses and large scale impulses are allowed to coexist. Finally, some examples are given to show the effectiveness of the obtained results.

Feedback Finite‐Time Stabilization of Impulsive Linear Systems over Piecewise Quadratic Domains

“…Lots of research results about Lyapunov stability for dynamical systems with impulsive effects have been developed (see, e.g., [6][7][8][9] and the references therein). Impulsive synchronization and control problems have attracted much research interest as well [10][11][12][13][14][15][16]. Furthermore, a variety of finite-time stability and stabilization problems are investigated for linear time-varying systems and impulsive linear systems [3,17,18].…”

Stabilization of Two Electricity Generators

“…ere are many kinds of nonlinearities which impede to reach the stabilization of electricity generators, and some examples of these nonlinearities are the arbitrary switching [9][10][11][12][13], the time-delays [14][15][16][17][18], the impulse perturbations [19,20], or the unknown nonlinearities [21][22][23][24]. e major issue is that in most of the cases, the mentioned nonlinearities are unknown.…”

Synchronization of a Generalized High-dimensional Kuramoto Model With Directed Graphs

“…Finally, an example is given to validate the theoretical results.Collective cooperative behavior occurs widely in nature, e.g., a flock of birds flying in a certain shape [38], the rhythmic flicker of fireflies[5], ants build nests and forage [24], and so on. Synchronization is a hot topic in collective behavior [7,19,25,28,31]. There are many mathematical models describing the synchronization phenomena, such as Winfree model [16], Vicsek model[40], a swarm sphere model [15] , Kuramoto model [22,23].…”