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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Angheluta-Bauer, Luiza / Chen, Xi / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi / Yang, Xu


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Volume 20, Issue 2

Issues

Representation of Solutions and Finite Time Stability for Delay Differential Systems with Impulsive Effects

Zhongli You
  • Department of Mathematics, School of Mathematics and Statistics, Guizhou University, Guiyang, Guizhou 550025, P.R. China
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/ JinRong Wang
  • Corresponding author
  • Department of Mathematics, School of Mathematics and Statistics, Guizhou University, Guiyang, Guizhou 550025, P.R. China
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/ Yong Zhou
  • Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, P.R. China; Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
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/ Michal Fečkan
  • Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia, and Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia
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Published Online: 2019-01-18 | DOI: https://doi.org/10.1515/ijnsns-2018-0137

Abstract

In this paper, we study finite time stability for linear and nonlinear delay systems with linear impulsive conditions and linear parts defined by permutable matrices. We introduce a new concept of impulsive delayed matrix function and apply the variation of constants method to seek a representation of solution of linear impulsive delay systems, which can be well used to deal with finite time stability. We establish sufficient conditions for the finite time stability results by using the properties of impulsive delayed matrix exponential and Gronwall’s integral inequalities. Finally, we give numerical examples to demonstrate the validity of theoretical results and present some possible advantage by comparing the current work with the previous literature.

Keywords: delay differential systems; impulsive effects; delayed exponential matrix; representation of solutions; finite time stability

MSC 2010: 34A37; 34D20

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About the article

Received: 2018-05-22

Accepted: 2018-12-16

Published Online: 2019-01-18

Published in Print: 2019-04-26


Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 20, Issue 2, Pages 205–221, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2018-0137.

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