Design of continuous linear control systems for minimum probabilistic error

A PREVIOUS PAPER1 has proposed the ¿probabilistic error¿ as measure of performance and basis of design for control systems. The probabilistic error or ¿end-sigma error¿ was defined as the average value of the suitably penalized error occurring at such times when the output of the system is actually utilized. This measure of performance was mathematically formulated1 and, for squared-error penalizing and invariant linear systems, was evaluated in a general way in the s or the t domain. An integral equation was also obtained1 which defines the optimum time invariant linear system in the sense that it has the smallest probabilistic error.