Exponential Stability of Linear Delay Impulsive Differential Equations

1993/11/26 by A. Anokhin, Leonid Berezansky, Anokhin, A. +3
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Opinion Dynamics and Social Influence #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.funct-an/9311004

openalex publication_date 1993/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For ordinary differential equations and functional differential equations the following result is well known. Suppose any solution is bounded on the half-line for each bounded on the half-line right-hand side. Then under certain conditions the equations is exponentially stable. We prove the same result for a delay differential equation x(t) + ∑_i=1^k A_i (t)x[h_i(t)] = f(t), with impulses x(τ_i + 0) = B_i x(τ_i - 0) at fixed moments τ_i. The proof is based on a solution representation formula obtained here.

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