Summary A performance criterion for feedback control systems is intro duced based on the averaging of penalized error values over such times when the output is actually utilized. This is accomplished by assigning a probability to the time of output utilization. The criterion is a suitable starting point of design since it unifies in one summary the various specifications normally used to de scribe special aspects of performance. Where the penalty is pro portional to the squared error, mathematical methods are de veloped for two roles: (1) evaluating the criterion for a given system operating in a known environment, and (2) designing the optimum time-invariant linear system, in the sense of giving the smallest average-penalized-error criterion value operating in a known input environment. An illustrative example is given. Survey of Performance Criteria A UTOMATIC CONTROL is, in one sense, at least as old as the first governors applied on early steam engines and, in another sense, as recent as World War II. As a field of engineering analysis and design, auto matic control, feedback control, and servomechanisms were developed in the years around the beginning of World War II as a specialty of electrical engineering. Considering that the major portion of most systems controlled is nonelectrical , the predominance of elec trical engineers in the early developing field of controls seems to be surprising. The reasons for this predomi nance are threefold. Among the members of the engi neering fraternity electrical engineers were equipped with some intuition in transient phenomena. Elec trical engineers had tools available for the analysis of feedback devices—that is, amplifiers. The necessary corrective devices were synthesized in the form of elec tric networks with the least difficulty in hardware and in theory of design. Performance criteria were from the beginning the guiding factors in the development of the field, and their gradual refinement simultaneously served as an index of the state of the art. The first criteria were characteristically indirect in nature. Since the early analysis and synthesis meth ods were borrowed from the field of feedback ampli fiers, the performance criteria were based on frequency response considerations;1-3 notably, sharpness and frequency location of resonance peaks were specified in