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Abstract This paper is concerned with the design of linear control systems so as to minimize some quadratic performance index. The method of design is applicable to both sampling and continuous control systems. Using the concepts of “state” and “transition matrix,” the design problem can be solved, via the technique of dynamic programming, by means of simple iterative computations. In this way, the classical Wiener method of design is extended in several different directions: (a) Using generalized performance indexes, (b) optimizing for classes of input signals rather than single inputs, (c) assuring stability of the optimally designed system.
Kalman et al. (Sat,) studied this question.