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Finite time stability of semilinear delay differential equations

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Abstract

In this paper, we study finite time stability for two classes of nonlinear delay differential equations, one is equation with a nonlinearity independent of delay and the other is equation with a nonlinearity depending on delay. Based on the solution structure involving delayed matrix exponential, sufficient conditions for the finite time stability results are derived by utilizing the properties of delayed matrix exponential and Gronwall integral inequalities under linear growth conditions for the nonlinear terms. Finally, we demonstrate the validity of designed method by using two numerical examples.

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Acknowledgements

The authors thanks the referees for their careful reading of the manuscript and insightful comments, which help to improve the quality of the paper. The authors thank the help from the editor too.

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Authors and Affiliations

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

    Zijian Luo & JinRong Wang

  2. College of Science, Guizhou Minzu University, Guiyang, 550025, Guizhou, People’s Republic of China

    Wei Wei

Authors
  1. Zijian Luo
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  2. Wei Wei
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Corresponding author

Correspondence to JinRong Wang.

Additional information

This work is partially supported by NNSF (No. 11661016), Training Object of High Level and Innovative Talents of Guizhou Province [(2016)4006], and Unite Foundation of Guizhou Province ([2015]7640).

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Luo, Z., Wei, W. & Wang, J. Finite time stability of semilinear delay differential equations. Nonlinear Dyn 89, 713–722 (2017). https://doi.org/10.1007/s11071-017-3481-6

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  • DOI: https://doi.org/10.1007/s11071-017-3481-6

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