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Global Power Stability of Neural Networks with Impulses and Proportional Delays

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Abstract

By establishing two new impulsive delay differential inequalities from impulsive perturbation and impulsive control point of view, respectively, constructing some Lyapunov functionals, and employing the matrix measure approach, some novel and sufficient conditions are obtained to guarantee global power stability of neural networks with impulses and proportional delays. The obtained stability criteria are dependent on impulses and the proportional delay factor so that it is convenient to derive some feasible impulsive control laws according to the proportional delay factor allowed by such neural networks. It is shown that impulses can act as stabilizers to globally power stabilize an unstable neural network with proportional delay based on suitable impulsive control laws. Moreover, the power convergence rate can be estimated and obtained by simple computation. Three numerical examples are given to illustrate the effectiveness and advantages of the results obtained.

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Acknowledgements

The author would like to thank the editor and the reviewers for a number of valuable comments and constructive suggestions that have improved the quality of this paper.

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Wuyi University, Jiangmen, 529020, Guangdong, China

    Kaizhong Guan

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  1. Kaizhong Guan
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Correspondence to Kaizhong Guan.

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Communicated by See Keong Lee.

This work is supported by the Natural Science Foundation of Guangdong Province, China (Nos. 2016A030313005 and 2015A030313643) and the Innovation Project of Department of Education of Guangdong Province, China (No. 2015KTSCX147).

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Guan, K. Global Power Stability of Neural Networks with Impulses and Proportional Delays. Bull. Malays. Math. Sci. Soc. 42, 2237–2264 (2019). https://doi.org/10.1007/s40840-018-0600-6

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  • DOI: https://doi.org/10.1007/s40840-018-0600-6

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