Synchronisation of complex dynamical networks with additive stochastic time-varying delays

Abstract

In this letter, a class of complex dynamical networks with additive stochastic time-varying delays is investigated. Two kinds of delays in complex dynamical networks are taken into consideration, one is called the nodes-induced delay in this paper, and the other is the network-induced delay. Both of the delays are assumed to obey different stochastic distributions. By utilising a novel Lyapunov–Krasovskii functional and stochastic analysis techniques, a sufficient criterion is obtained in the form of linear matrix inequalities to ensure the synchronisation of the complex dynamical networks. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.

Keywords:

• complex dynamical network
• additive delay
• stochastic distribution
• synchronisation

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grants 61374171 and 61074124, the Program for Changjiang Scholars and Innovative Research Team in University (IRT1245), and Graduates’ Innovation Fund of Huazhong University of Science and Technology (HF-11-18-2013).

Additional information

Notes on contributors

Jing-Wen Yi

Jing-Wen Yi received the MS degree in automatic control from Yantai University, Yantai, China, in 2010, and now is studying control theory and control engineering for her PhD degree in Huazhong University of Science and Technology (HUST), Wuhan, China. Her current research interests include complex networks and hybrid systems.

Yan-Wu Wang

Yan-Wu Wang received the BS degree in automatic control, the MS degree and the PhD degree in control theory and control engineering from HUST in 1997, 2000 and 2003, respectively. From 2003 to 2005, she worked as a postdoctoral researcher in the Department of Electronics and Information Engineering, HUST. From February to April, 2005, she held the visiting position with the School of Electrical and Electronic Engineering in Nanyang Technological University. From September 2008 to September 2009, she held the position of visiting scholar with the Department of Mechanical Engineering in Boston University. Since November 2009, she has been a professor in the Department of Control Science and Engineering, HUST. Her current research interests include complex networks and hybrid systems. Dr Wang is a recipient of the 2006 Natural Science Award of Ministry of Education Nominated State Science and Technology Award, China, the 2005 Natural Science Award of Hubei Province, China, and the 2004 Excellent PhD Dissertation of Hubei Province, China. In 2008, she was awarded the title of New Century Excellent Talents by the Chinese Ministry of Education.

Jiang-Wen Xiao

Jiang-Wen Xiao received the BS degree in electrical engineering, the MS degree in control theory and control engineering, and the PhD degree in systems engineering from HUST, Wuhan, China, in 1994, 1997 and 2001, respectively. From 2001 to 2003, he worked as a postdoctoral researcher in the College of Management, HUST, Wuhan, China. Since July 2003, he has been an associate professor in the Department of Control Science and Engineering, HUST. His current research interests include modelling and control of nonlinear and complex systems.

Yuehua Huang

Yue-Hua Huang is the dean and professor in the College of Electrical Engineering and New Energy, China Three Gorges University. He is the academic leader of control theory and control engineering in China Three Gorges University. He has presided over more than 20 projects of the vertical and horizontal scientific research, including 2 national projects. He has published more than 40 papers, in which more than 20 papers are included by three major search indexes (SCI, EI and ISTP). His main research directions are network system control and safety, motor and its control, new energy microgrid, intelligent devices and detection technology.