Adaptive synchronization of complex dynamical networks in presence of coupling connections with dynamical behavior

[+] Author and Article Information
Ali Kazemy

Department of Electrical Engineering, Tafresh University, Tafresh 39518-79611, Iran

Khoshnam Shojaei

Department of Electrical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

1Corresponding author.

ASME doi:10.1115/1.4043146 History: Received July 14, 2018; Revised March 06, 2019


In this paper, the synchronization of complex dynamical networks (CDNs) is investigated, where coupling connections are expressed in terms of state-space equations. As it is shown in simulation results, such links can greatly affect the synchronization and cause synchronization loss, while many real-world networks have these types of connections. With or without time-delay, two different models of the CDNs are presented. Then, by introducing a distributed adaptive controller, the synchronization conditions are derived by utilizing the Lyapunov(-Krasovskii) theorem. These conditions are provided in the form of linear matrix inequalities (LMIs) which can be easily solved by standard LMI solvers even for large networks due to a few numbers of scalar decision variables. At the end, illustrative numerical examples are given to specify the effectiveness of the proposed methods.

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