2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152325For 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 $$ \dot{x}(t) + \sum_{i=1}^k A_i (t)x[h_i(t)] = f(t), $$ 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.29 pp., LaTex-fileFunctional AnalysisDynamical Systemstext