Adaptive lag synchronization for competitive neural networks with mixed delays and uncertain hybrid perturbations

Authors:
Xinsong Yang;Jinde Cao;Yao Long;Weiguo Rui
Affiliations:
Department of Mathematics, Honghe University, Mengzi, Yunnan, China;Department of Mathematics, Southeast University, Nanjing, China;Department of Mathematics, Honghe University, Mengzi, Yunnan, China;Department of Mathematics, Honghe University, Mengzi, Yunnan, China
Venue:
IEEE Transactions on Neural Networks
Year:
2010

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Abstract

This paper investigates the problem of adaptive lag synchronization for a kind of competitive neural network with discrete and distributed delays (mixed delays), as well as uncertain nonlinear external and stochastic perturbations (hybrid perturbations). A simple but robust adaptive controller is designed such that the response system can lag-synchronize with a drive system. Based on the Lyapunov stability theory and some suitable Lyapunov-Krasovskii functionals, several sufficient conditions ensuring the lag synchronization are developed. Our synchronization criteria are easily verified and do not need to solve any linear matrix inequality. Some existing results are improved and extended. Moreover, the designed adaptive controller has better anti-interference capacity and is more practical than the usual adaptive controller. Numerical simulations are exploited to show the effectiveness of the theoretical results.