Exponential Synchronization for Second-Order Nodes in Complex Dynamical Network with Communication Time Delays and Switching Topologies

Abstract

This paper is devoted to the study of exponential synchronization problem for second-order nodes in dynamical network with time-varying communication delays and switching communication topologies. Firstly, a decomposition approach is employed to incorporate the nodes’ inertial effects into the distributed control design. Secondly, the sufficient conditions are provided to guarantee the exponential synchronization of second-order nodes in the case that the information transmission is delayed and the communication topology is balanced and arbitrarily switched. Finally, to demonstrate the effectiveness of the proposed theoretical results, it is applied to the typical second-order nodes in dynamical network, as a case study. Simulation results indicate that the proposed method has a high performance in synchronization of such network.

Adaptive Output Synchronization of General Complex Dynamical Network with Time-Varying Delays

“…It is almost impossible to learn the exact information of strength between cells or time delays, especially for a large-scale network. The existences of time delays can deteriorate the control performance and cause instability, see, e.g., [21][22][23][24][25][26][27][28][29]. In [21], an adaptive feedback strategy is proposed for a class of Takagi-Sugeno fuzzy complex networks with unknown topological structure and distributed time-varying delay, and the designed controller is only related to the dynamic behavior of directly related nodes.…”

“…In [21], an adaptive feedback strategy is proposed for a class of Takagi-Sugeno fuzzy complex networks with unknown topological structure and distributed time-varying delay, and the designed controller is only related to the dynamic behavior of directly related nodes. The authors of [22] researched the exponential synchronization of second-order nodes in dynamic networks with time-varying communication delays and switched communication topologies. The problem of synchronization control of complex dynamic networks with time-varying delays is studied in [27], a study in which is designed the synchronization controller of sampling system, which can make the generated synchronization error system stable.…”

Analysis and Design of Adaptive Synchronization of a Complex Dynamical Network with Time-Delayed Nodes and Coupling Delays

“…In these investigations, an essential requirement is that the structure of the networks and the coupling functions are known beforehand. In order to overcome the aforementioned constraints, synchronization in complex networks by controller methods has also been investigated [21][22][23][24]. Zhou et al [21] proposed some synchronization criteria and designed simple controllers for several specific complex networks.…”

“…Based on the leader-follower model, Zhou et al [23] proposed an improved network structure model for realizing the cluster synchronization on multiple subnetworks of complex networks, and some suitable pinning controllers on the chosen nodes of each follower's subnetwork are designed. Yu et al [24] employed a decomposition approach to incorporate the nodes' inertial effects into the distributed control design for second-order nodes in a dynamical network with communication delays and switching communication topologies.…”