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In this paper and in a companion paper a technique for the synthesis of linear, nonstationary feedback systems is presented. This paper deals with the approximation problem, i.e., a method is developed whereby a realizable weighting function which produces a desired output when subjected to a polynomial input can be generated. Certain conditions which must be fulfilled by the outputs are also developed.
In this paper and in a companion paper a technique for the synthesis of linear, nonstationary feedback systems is presented. This paper deals with the synthesis problem, i.e., a method is developed whereby a given weighting function can be synthesized as a feedback system. The problem of synthesizing a nonstationary weighting function as a feedback system when constrained by a fixed plant is also solved. A differential equation algebra which allows the solution of these problems is produced.