Rε represents a linear time-invariant system of order n + h. When ε → 0, Rε, reduces to R0 of order n ≤ n + h. Conditions are given under which the bounded-input bounded-state stability of R0 implies that of Rε and we show that, under these conditions, as ε → 0, the state trajectories of Rε approach those of R0 for any continuous input.