In this paper we focus our attention on the determination of upper bounds of the l(infinity) norm of the output of a linear discrete-time dynamic system driven by a step input, in the presence of both persistent unknown, but, l(infinity) bounded disturbances and memoryless time-varying model uncertainty. For the same type of systems we also analyze the transient behavior of the step response in terms of its overshoot. The problem is solved in a constructive way by determining appropriate invariant sets contained in a given convex region. Finally, we show how to extend these results to continuous-time systems.