Impulsive Stabilization of Linear Delay Differential Equations

1995/02/21 by Leonid Berezansky, Berezansky, L., Elena Braverman +1
Engineering · Mathematics · Medicine · #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.funct-an/9502005

openalex publication_date 1995/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper is concerned with stabilization of a scalar delay differention equation x(t) - ∑_k=1^m A_k(t)x[h_k(t)] = 0,~t≥ 0,~ x(ξ)=φ(ξ), ξlt;0, by introducing impulses in certain moments of time x(τ_j) = B_j x(τ_j -0), ~j=1,2, … ~. Explicit stability results are presented both for the equation with positive coefficients and for the equation with A_k being of arbitrary sign.

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