ASYMPTOTIC CONSTANCY FOR IMPULSIVE DELAY DIFFERENTIAL EQUATIONS

Sufficient conditions for the asymptotic constancy of the solutions of impulsive delay differential system ( x 0 (t) = A(t)[x(t − σ) − x(t − τ )] + f(t), t ≥ t0, t 6= ti , ∆x(ti) = Bix(ti) + Di , i = 1, 2, . . . , are obtained. Moreover, as t → ∞, the limits of the solutions of the impulsive delay differential system with Bi = 0 are computed in terms of the initial function and a special matrix solution of the corresponding adjoint system.