Generating Globally Stable Periodic Solutions of Delayed Neural Networks With Periodic Coefficients via Impulsive Control

IEEE Transactions on Cybernetics
Wu-Hua Chen Wei Xing Zheng

Abstract

This paper is dedicated to designing periodic impulsive control strategy for generating globally stable periodic solutions for periodic neural networks with discrete and unbounded distributed delays when such neural networks do not have stable periodic solutions. Two criteria for the existence of globally exponentially stable periodic solutions are developed. The first one can deal with the case where no bounds on the derivative of the discrete delay are given, while the second one is a refined version of the first one when the discrete delay is constant. Both stability criteria possess several adjustable parameters, which will increase the flexibility for designing impulsive control laws. In particular, choosing appropriate adjustable parameters can lead to partial state impulsive control laws for certain periodic neural networks. The proof techniques employed includes two aspects. In the first aspect, by choosing a weighted phase space PCα, a sufficient condition for the existence of a unique periodic solution is derived by virtue of the contraction mapping principle. In the second aspect, by choosing an impulse-time-dependent Lyapunov function/functional to capture the dynamical characteristics of the impulsively controlled ...Continue Reading

Citations

Apr 20, 2017·IEEE Transactions on Cybernetics·Xian-Ming ZhangBao-Lin Zhang
Jun 23, 2021·Neural Networks : the Official Journal of the International Neural Network Society·Zuowei CaiShukun Liu

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