Maximum output amplitude of linear systems for certain input constraints

We determine the maximum output amplitude of a system, when the input is bounded by certain constraints. In particular, amplitude and rate of change (i.e. the first derivative) have to be bounded. We show properties of the worst case input and present an algorithm that allows construction of this input and calculates the maximum amplitude of the output. The solution of this problem is a necessary and important step within a couple of recently developed controller-design procedures, dealing with plants with hard-bounded inputs. Nevertheless, it is interesting as a system theoretic task itself and therefore stated separately