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Stability of Variable-Time Impulsive Systems with Delays via Generalized Razumikhin Technique and Application to Impulsive Neural Networks

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Abstract

This paper investigates the stability of variable-time impulsive systems with time delays. A novel stability result is obtained via the generalized Razumikhin technique. By viewing fixed-time impulsive systems as degenerative variable-time impulsive systems, a new stability result for fixed-time impulsive systems is also proposed. In order to demonstrate the effectiveness of the generalized Razumikhin technique, we give some comparison results with the existing stability criteria which are derived from the classical Razumikhin technique. Stability of impulsive neural networks and synchronization of complex networks are employed to indicate the effectiveness and the practicality of the theoretical results.

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Acknowledgements

This project is supported by National Natural Science Foundation of China (Grant Nos. 61503052, 61503050, 61603065, 11647097 and 11547148), Research Foundation of the Natural Foundation of Chongqing City (Grant Nos. cstc2014jcyjA40024, cstc2014jcyjA40007, cstc2016jcyjA0076 and cstc2013jcyjA40019), Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant Nos. KJ1600928, KJ1501301, KJ1500918, KJ1500904, KJ1500926 and KJ1600923) and Young Fund of Humanities and Social Sciences of the Ministry of Education of China (Grant Nos. 16JDSZ2019, 16YJC870018, 16YJC860010 and 15YJC790061).

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Authors and Affiliations

  1. Postdoctoral Research Station of Control Science and Engineering, Chongqing University, Chongqing, 400044, People’s Republic of China

    Chao Liu

  2. School of Computer Science and Engineering, Chongqing University of Technology, Chongqing, 400054, People’s Republic of China

    Chao Liu & Xiaoyang Liu

  3. College of Automation, Chongqing University, Chongqing, 400044, People’s Republic of China

    Dihua Sun

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  1. Chao Liu
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  2. Dihua Sun
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  3. Xiaoyang Liu
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Correspondence to Chao Liu.

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Liu, C., Sun, D. & Liu, X. Stability of Variable-Time Impulsive Systems with Delays via Generalized Razumikhin Technique and Application to Impulsive Neural Networks. Neural Process Lett 47, 641–659 (2018). https://doi.org/10.1007/s11063-017-9673-8

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  • DOI: https://doi.org/10.1007/s11063-017-9673-8

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