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Pinning impulsive synchronization of complex dynamical networks with various time-varying delay sizes
Affiliation:1. School of Information Science and Engineering, Chengdu University, Chengdu, 610106, China;2. Department of Computer and Information Science, Faculty of Science and Technology, University of Macau, Taipa 853, Macau, China;3. Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1, Canada;4. School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China;5. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China;1. School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China;2. Department of Applied Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada;3. School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth, WA 6845, Australia;1. School of Automation, Guangdong University of Petrochemical Technology, Maoming 525000, PR China;2. School of Electrical Engineering, The University of Adelaide, Adelaide 5005, SA, Australia;3. School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640, PR China;1. Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, PR China;2. School of Information Engineering, Huzhou University, Huzhou 313000, China;3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;4. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia;1. Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada;2. Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Abstract:This paper studies the pinning impulsive synchronization problem for a class of complex dynamical networks with time-varying delay. By applying the Lyapunov stability theory and mathematical analysis technique, sufficient verifiable criterion for the synchronization of delayed complex dynamical networks with small delay is derived analytically. It is shown that synchronization can be achieved by only impulsively controlling a small fraction of network nodes. Moreover, a novel sufficient condition is constructed to relax the restrictions on the size of time-delay and guarantee the synchronization of concerned networks with large delay. Two numerical examples are presented to illustrate the effectiveness of the obtained results.
Keywords:Synchronization  Complex dynamical networks  Pinning impulsive control  Time-varying delay
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