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

  • Zhongli You , JinRong Wang EMAIL logo , Yong Zhou and Michal Fečkan

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.

MSC 2010: 34A37; 34D20

Acknowledgements

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

This work was partially supported by National Natural Science Foundation of China (11661016, 11671339), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), Science and Technology Program of Guizhou Province ([2017]5788-10), Major Research Project of Innovative Group in Guizhou Education Department ([2018]012), Foundation of Postgraduate of Guizhou Province (YJSCXJH[2018]035), and the Slovak Research and Development Agency under the Contract No. APVV-14-0378 and by the Slovak Grant Agency VEGA No. 2/0153/16 and No. 1/0078/17.

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Received: 2018-05-22
Accepted: 2018-12-16
Published Online: 2019-01-18
Published in Print: 2019-04-26

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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