A Lyapunov-like theorem is presented for finding an upper estimate on the set of points in Rn which are reachable from an initial set of continuous functions φ:[−r, 0] → Rn which satisfy sup[−r, 0]|φ(s)| < δ where the dynamics of the system are governed by n first order retarded functional differential equations with bounded delay subject to bounded control. An example is given for a second order delay-differential equation.

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