Stability of impulsive delay differential equations
type: Item
instance of: scholarly article
title: Stability of impulsive delay differential equations
zbMATH Open document ID: 1388.34072
author: Zhongli You
author: Jinrong Wang
published in: Journal of Applied Mathematics and Computing
publication date: 2018-04-13T00:00:00Z
review text: In this paper, the authors introduce the impulsive delayed Cauchy matrix and seek the formula of solutions for the following linear impulsive delay differential equation \[ \begin{aligned} \dot x(t) & = Ax(t)+Bx(t-\tau),\quad t\geq0, \tau>0, t\neq t_i,\\ \Delta x(t_i) & = C_ix(t_i),\quad i=1, 2, \dots,\\ x(t) & = \varphi(t), \quad -\tau\leq t\leq0,\end{aligned} \] where \(A, B, C_i\) are constant matrices, \(AB=BA\), \(AC_i=C_iA\) and \(BC_i=C_iB\) for each \(i=1, 2,\dots\), \(\varphi\in C^1([-\tau, 0], \mathbb{R}^n)\), \(x(t)\in \mathbb{R}^n\), and time sequences \(\{t_k\}_{k=1}^{\infty}\) satisfy \(0=t_0<t_1<\dots<t_k<\dots\), \(\Delta x(t_k)=x(t_k^+)-x(t_k^-)\).
Mathematics Subject Classification ID: 34K45
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K06
zbMATH DE Number: 6859484
zbMATH Keywords: impulsive delayed Cauchy matrix
zbMATH Keywords: impulsive delay differential equations
reviewed by: Alexander O. Ignatyev
MaRDI profile type: Publication
full work available at URL: s12190-016-1072-1
OpenAlex ID: W2558870600
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DOI: 10.1007/S12190-016-1072-1
description: scientific article; zbMATH DE number 6859484