Impulsive Stabilization of Linear Delay Differential Equations

L. Berezansky; E. Braverman

Impulsive Stabilization of Linear Delay Differential Equations

funct-an 2008-02-03 v1 Dynamical Systems Functional Analysis

Authors: L. Berezansky , E. Braverman

Abstract

The paper is concerned with stabilization of a scalar delay differention equation ${\dot x}(t) - \sum_{k=1}^m A_k(t)x[h_k(t)] = 0,~t\geq 0,~ x(\xi)=\varphi (\xi), \xi <0,$ by introducing impulses in certain moments of time $x(\tau_j) = B_j x(\tau_j -0), ~j=1,2, \dots ~.$ Explicit stability results are presented both for the equation with positive coefficients and for the equation with $A_k$ being of arbitrary sign.

Keywords

delay differential equations stability theory

Cite

@article{arxiv.funct-an/9502005,
  title  = {Impulsive Stabilization of Linear Delay Differential Equations},
  author = {L. Berezansky and E. Braverman},
  journal= {arXiv preprint arXiv:funct-an/9502005},
  year   = {2008}
}