\input zb-basic \input zb-ioport \iteman{io-port 03976901} \itemau{Henr\'{\i}quez, Hern\'an R.} \itemti{Asymptotic stability properties of self-accessible control systems.} \itemso{Recent advances in system modelling and optimization, Proc. IFIP-WG 7/1 Work. Conf., Santiago/Chile 1984, Lect. Notes Control Inf. Sci. 87, 142-147 (1986).} \itemab [For the entire collection see Zbl 0601.00015.] We establish some relations between the concept of self-accessibility and the asymptotic behaviour of trajectories for linear time-invariant systems. \itemrv{~} \itemcc{} \itemut{self-accessibility; asymptotic behaviour of trajectories; linear time- invariant systems; time-invariant} \itemli{} \end