Asymptotic stability of solutions of impulsive multi-delay differential equations

被引：6
作者：
You, Zhongli [1 ]
Wang, JinRong [1 ,2 ]
O'Regan, D. [3 ]
机构：
[1] Guizhou Univ, Dept Math, Guiyang 550025, Guizhou, Peoples R China
[2] Key & Special Lab Syst Optimizat & Sci Comp Guizh, Guiyang, Guizhou, Peoples R China
[3] Natl Univ Ireland, Sch Math Stat & Appl Math, Galway, Ireland
来源：
TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL | 2018年 / 40卷 / 15期
基金：
中国国家自然科学基金;
关键词：
Impulsive differential equations; multiple delays; impulsive multi-delayed Cauchy matrix; solution; asymptotic stability; LINEAR DISCRETE-SYSTEMS; PURE DELAY; CONSTANT-COEFFICIENTS; CONTROLLABILITY; REPRESENTATION; MATRICES;
D O I：
10.1177/0142331217742966
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we consider the asymptotic stability of solutions to impulsive multi-delayed differential equations with linear parts defined by pairwise permutable matrices. First, we introduce the concept for an impulsive multi-delayed Cauchy matrix and then use it to obtain the representation of solutions to linear impulsive Cauchy problems via the variation of constants principle. Next, we give a norm estimate of the impulsive multi-delayed Cauchy matrix and establish sufficient conditions to guarantee that the trivial solutions are asymptotically stable when the nonlinear terms satisfy appropriate conditions. Finally, two numerical examples are given to illustrate the effectiveness of the results.
引用
收藏
页码：4143 / 4152
页数：10
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