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Positivity and Exponential Stability of Coupled Homogeneous Time-Delay Differential–Difference Equations of Degree One

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Abstract

This paper investigates the global exponential stability of coupled homogeneous positive time-delay differential–difference equations of degree one. By using max-separable Lyapunov functions, a sufficient criterion for coupled homogeneous positive time-delay differential–difference equations of degree one is obtained. It should be noted that it is the first time that the exponential stability result for coupled homogeneous positive time-delay differential–difference equations of degree one is given. A numerical example is presented to demonstrate the effectiveness of the derived results.

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Acknowledgements

The authors would like to thank the editor and the anonymous reviewers for their constructive comments and suggestions which improved the quality of the paper. This work was supported by the Foundation of Key Laboratory of Advanced Process Control for Light Industry (Jiangnan University), Ministry of Education, P.R. China (No. APCLI2002), Scientific Research Foundation of Education Bureau of Jiangxi Province (No. GJJ201020) and Ph.D. Research Initiation Project of Jinggangshan University (JZB2021).

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Authors and Affiliations

  1. School of Mathematics and Physics, Jinggangshan University, Ji’an, 343009, China

    Huitao Yang & Xuan Huang

  2. School of Mathematical Sciences, Tongji University, Shanghai, 200092, China

    Yu Zhang & Shanshan Hong

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  1. Huitao Yang
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  2. Yu Zhang
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  3. Xuan Huang
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  4. Shanshan Hong
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Correspondence to Yu Zhang.

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Yang, H., Zhang, Y., Huang, X. et al. Positivity and Exponential Stability of Coupled Homogeneous Time-Delay Differential–Difference Equations of Degree One. Circuits Syst Signal Process 41, 762–788 (2022). https://doi.org/10.1007/s00034-021-01828-0

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