Synchronisation analysis for coupled networks with multiple delays

Abstract

This paper concerns the synchronisation problems for coupled networks with multiple time-varying delays. By linearising complicated system to some time-delayed subsystems, some novel criteria are given to ensure the robust synchronisation for the complex systems with multiple delays. Moreover, the presented results are also applied to the system with single time delay, and the coupling configuration matrix is not necessarily symmetric. Since the results are expressed in the form of linear matrix inequality , the obtained criteria can be easily checked in practice. Finally, numerical examples are provided to show the effectiveness of the obtained results.

Keywords:

• neural networks
• synchronisation
• multiple delays
• time-varying delays

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61104021], [grant number 51305066]; the National Science Fund for Distinguished Young Scholar [grant number 51225503]; Post-doctoral Foundation of China [grant number 2013M531945].

Notes on contributors

Xiaolin Dai

Xiaolin Dai received his BS, ME and PhD degree from the Harbin Institute of Technology, Harbin, in 1999, 2001 and 2009, respectively. Currently, he is with the School of Mechatronics Engineering, University of Electronic Science and Technology of China, Chengdu, China. His research interests include analysis and control of parallel manipulators.

Dawei Gong

Dawei Gong received his PhD degree in control theory and control engineering from Northeastern University, Shenyang, China, in 2012. Currently, he is a lecturer at the University of Electronic Science and Technology of China, Chengdu, China. His current research interests include neural networks, complex networks, fuzzy modelling and control, optimisation in process industries and intelligent optimisation algorithms.

Bonan Huang

Bonan Huang received his BS and MS degree in control theory and control engineering from Tianjin University in 2005 and Northeastern University in 2006, China, respectively. He is pursuing his PhD degree in control theory and control engineering at Northeastern University, China. His current research interests include neural networks and their applications in intelligent control, computational intelligence and optimisation theory.

Junjie Li

Junjie Li received his BS degree from Northwest A&F University in 2011. Currently, he is pursuing his MS degree in mechatronics engineering at the University of Electronic Science and Technology of China, Chengdu, China. His research interests include analysis and design of mechanical structure.