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

被引：5

作者：

You, Zhongli ^{[1
]}

Wang, JinRong ^{[1
]}

Zhou, Yong ^{[2
,3
]}

Feckan, Michal ^{[4
,5
]}

机构：

[1] Guizhou Univ, Sch Math & Stat, Dept Math, Guiyang 550025, Guizhou, Peoples R China

[2] Xiangtan Univ, Dept Math, Xiangtan 411105, Hunan, Peoples R China

[3] King Abdulaziz Univ, Fac Sci, Nonlinear Anal & Appl Math NAAM Res Grp, Jeddah 21589, Saudi Arabia

[4] Comenius Univ, Fac Math Phys & Informat, Dept Math Anal & Numer Math, Bratislava 84248, Slovakia

[5] Slovak Acad Sci, Inst Math, Stefanikova 49, Bratislava 81473, Slovakia

来源：

INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION | 2019年 / 20卷 / 02期

基金：

中国国家自然科学基金;

关键词：

delay differential systems; impulsive effects; delayed exponential matrix; representation of solutions; finite time stability; LINEAR DISCRETE-SYSTEMS; INTEGRAL-INEQUALITIES; CONSTANT-COEFFICIENTS; ASYMPTOTIC STABILITY; NEURAL-NETWORKS; EQUATIONS; PARTS; CONTROLLABILITY;

D O I：

10.1515/ijnsns-2018-0137

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

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.

引用

页码：205 / 221

页数：17

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