title: Exponential synchronization of discontinuous neural networks with time-varying mixed delays via state feedback and impulsive control.
abstract: This paper investigates drive-response synchronization for a class of neural networks with time-varying discrete and distributed delays (mixed delays) as well as discontinuous activations. Strict mathematical proof shows the global existence of Filippov solutions to neural networks with discontinuous activation functions and the mixed delays. State feedback controller and impulsive controller are designed respectively to guarantee global exponential synchronization of the neural networks. By using Lyapunov function and new analysis techniques, several new synchronization criteria are obtained. Moreover, lower bound on the convergence rate is explicitly estimated when state feedback controller is utilized. Results of this paper are new and some existing ones are extended and improved. Finally, numerical simulations are given to verify the effectiveness of the theoretical results.
authors.affiliation: Department of Mathematics, Chongqing Normal University, Chongqing, 401331 China.
authors.forename: Xinsong
authors.initials: X
authors.lastname: Yang
authors.affiliation: Department of Mathematics, Southeast University, Nanjing, 210096 China ; Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589 Saudi Arabia.
authors.forename: Jinde
authors.initials: J
authors.lastname: Cao
authors.affiliation: Department of Mathematics, City University of Hong Kong, Hong Kong, China ; School of Automation, Nanjing University of Science and Technology, Nanjing, 210096 China.
authors.forename: Daniel W C
authors.initials: DW
authors.lastname: Ho
keywords: Discontinuous activations; Exponential synchronization; Filippov solutions; Impulsive control; Neural networks; State feedback control
references.citation: Cogn Neurodyn. 2011 Jun;5(2):133-43
references.pmid: 22654986
references.citation: Cogn Neurodyn. 2009 Mar;3(1):47-81
references.pmid: 19003467
references.citation: Cogn Neurodyn. 2014 Dec;8(6):465-78
references.pmid: 26396646
references.citation: Neural Netw. 2011 Dec;24(10):1013-21
references.pmid: 21764257
references.citation: Cogn Neurodyn. 2013 Feb;7(1):59-65
references.pmid: 24427191
references.citation: Neural Netw. 2009 Sep;22(7):931-7
references.pmid: 19443177
references.citation: Neural Netw. 2014 Apr;52:25-32
references.pmid: 24469328
references.citation: Cogn Neurodyn. 2014 Jun;8(3):239-49
references.pmid: 24808932
references.citation: IEEE Trans Neural Netw. 2005 Nov;16(6):1449-63
references.pmid: 16342487
references.citation: Neural Comput. 2008 Apr;20(4):1065-90
references.pmid: 18085989
references.citation: Phys Rev Lett. 1990 Feb 19;64(8):821-824
references.pmid: 10042089
references.citation: Neural Netw. 2014 May;53:165-72
references.pmid: 24632220
references.citation: Proc Natl Acad Sci U S A. 1987 Apr;84(7):1896-900
references.pmid: 3470765