Fast synchronization of complex dynamical networks with time-varying delay via periodically intermittent control

Abstract

The fast synchronization problem for a class of complex dynamical networks with time varying delay by means of periodically intermittent control is studied. Based on the finite-time stability theory and periodically intermittent control technique, some sufficient synchronization criteria are obtained to guarantee the fast synchronization. Furthermore, the essential condition for guaranteeing periodically intermittent control realized in finite time is given in this paper. Finally, two examples are illustrated to verify the proposed theoretical results.

Exponential Synchronization of Neural Networks via Feedback Control in Complex Environment

“…It is noted that the results of [35][36][37][38][39] are valid with periodically intermittent control. While in this paper, Theorem 1 is effective with aperiodically intermittent control, which is more general and flexible than that of [35][36][37][38][39]. On the other hand, in [29][30][31][32][33][34], the transmittal time is ignored when constructing the controller.…”

“…Therefore, intermittent control combines the advantages of impulsive control and continuous feedback control. In the past decade, many valuable results have been obtained for synchronization of neural networks under intermittent control [35][36][37][38][39]. For example, by applying the average dwell time approach, structuring multiple Lyapunov-Krasovskii functions, and using Halanay inequality, new robust synchronization criteria are obtained for switched coupled networks via intermittent control [35].…”

“…For example, by applying the average dwell time approach, structuring multiple Lyapunov-Krasovskii functions, and using Halanay inequality, new robust synchronization criteria are obtained for switched coupled networks via intermittent control [35]. In [36], the fast synchronization problem for a class of complex dynamical networks with time varying delay by means of periodically intermittent control was investigated. By designing appropriate adaptive intermittent controllers and using the Lyapunov stability theory, some pinning outer synchronization criteria are derived in [37], which can guarantee that the response network asymptotically synchronizes to the drive network.…”

Exponential Synchronization of Dynamical Network with Distributed Delays Via Intermittent Control

“…Meanwhile, lots of network models have been introduced to describe the real world. In particular, synchronization is an interesting and important collective phenomena in networks and has been deeply investigated . The research on synchronization can be tracked to the most important work of Huygens about pendulum clocks in the 17th century.…”

“…For any given dynamical network, the key point for designing intermittent controllers is to derive the synchronization conditions with respect to the control rate, control gains and system parameters. Recently, many valuable results about intermittent control are obtained [17][18][19][20][21][22][23][24][25][26][27][28][29][30]. In Refs.…”