Representation of Solutions and Finite Time Stability for Delay Differential Systems with Impulsive Effects-Reference-Cited by-同舟云学术

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

Published:2019-01-18 Issue:2 Volume:20 Page:205-221
ISSN:2191-0294
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
language:en
Short-container-title:

Author:

You Zhongli¹,Wang JinRong¹,Zhou Yong²,Fečkan Michal³

Affiliation:

1. Department of Mathematics , School of Mathematics and Statistics, Guizhou University , Guiyang , Guizhou 550025 , P.R. China

2. 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

3. 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

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modelling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ijnsns-2018-0137/pdf

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