On matrix differential equations with several unbounded delays

摘要

The paper focuses On the matrix differential equation y(t) = A(t)y(t) + Sigma B-m(j=1)j(t)y(tau(j)(t)) + f(t), t is an element of I = [t(0),infinity) with continuous matrices A, B-j, a continuous vector f and continuous delays tau(j) satisfying tau(k) circle tau(j) = tau(j) circle tau(k) on I for any pair tau(k), tau(j). Assuming that the equation y(t) = A(t)y(t) is uniformly exponentially stable, we present some asymptotic bounds of solutions y of the considered delay equation. A system of simultaneous Schroder equations is used to formulate these asymptotic bounds.