The principle of matching: practical conditions for systems with inputs restricted in magnitude and rate of change

The main objective of matching, a principle of design, is to ensure that the set of possible inputs to a system is a subset of the set of tolerable inputs (those which are judged to produce an acceptable response from the system). This note presents practical conditions (some necessary and sufficient, and others only sufficient) for a matched design, when the set of possible inputs is characterized by restrictions on the magnitude and the rate of change of the input, and the set of tolerable inputs is characterized by magnitude bounds on the response of the system