A principle for the design of control systems, called matching, requires primarily that the set of all possible inputs to a system is a subset of the set of all tolerable inputs (those which are judged to produce an acceptable response). In this paper, a readily computable necessary and sufficient condition for matching is provided for the case in which the tolerable set is defined by uniform bounds on the magnitude of outputs, and the possible set is defined by separate restrictions on the integral square of the input and the integral square of the input’s rate of change. An example of a matched design obtained using the condition is given.