Asymptotic property for linear integro-differential systems

We study the asymptotic property of linear integro-differential systems by means of the resolvent matrices and the useful equivalent system of Rao and Srinivas in [M.R.M. Rao, P. Srinivas, Asymptotic behavior of solutions of Volterra integro-differential equations, Proc. Amer. Math. Soc. 94 (1985) 55–60. [11]].