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Representation and Stability of Solutions for Impulsive Discrete Delay Systems with Linear Parts Defined by Non-Permutable Matrices

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Abstract

In this paper, we introduce a modified delayed perturbation of discrete matrix exponential for impulsive linear discrete delay systems with non-permutable matrices. Using the \({\mathcal {Z}}\)-transform method and its alternative method, we derive a clear representation of the solution, which covers both impulsive and non-impulsive cases in the existing literature. Moreover, using the representation of solution, discrete Gronwall’s inequality, and discrete Bihari’s inequality, we establish several results of exponential stability. Numerical examples are given to verify these results.

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Acknowledgements

The authors are grateful to the referees for their careful reading of the manuscript and valuable comments. The authors thank the help from the editor too.

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Authors and Affiliations

  1. Department of Mathematics, Guizhou University, Guiyang, Guizhou, 550025, People’s Republic of China

    Xianghua Jin & JinRong Wang

  2. School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian, 362021, People’s Republic of China

    Xianghua Jin

  3. School of Mathematics, Renmin University of China, Beijing, 100872, People’s Republic of China

    Dong Shen

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  1. Xianghua Jin
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  2. JinRong Wang
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  3. Dong Shen
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Correspondence to JinRong Wang.

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This work is partially supported by the National Natural Science Foundation of China (12161015), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), Guizhou Data Driven Modeling Learning and Optimization Innovation Team ([2020]5016), and Super Computing Algorithm and Application Laboratory of Guizhou University and Gui’an Scientific Innovation Company (K22-0116-003).

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Jin, X., Wang, J. & Shen, D. Representation and Stability of Solutions for Impulsive Discrete Delay Systems with Linear Parts Defined by Non-Permutable Matrices. Qual. Theory Dyn. Syst. 21, 152 (2022). https://doi.org/10.1007/s12346-022-00685-9

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  • DOI: https://doi.org/10.1007/s12346-022-00685-9

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