A METHOD FOR GENERAL DESIGN OF POSITIVE REAL FUNCTIONS

The objective of this brief is to develop a general method for the syn thesis of a solution to the problem of designing positive real functio ns of a prefixed Hurwitz denominator polynomial. Such a synthesis prob lem is reduced to the calculation of the solution of an equivalent alg ebraic system of linear equations. The dual problem of designing the d enominator polynomial for a prefixed given numerator polynomial is als o focused on. The problem is first solved for rational realizable func tions and extended in a natural way to nonrational ones by simply addi tion of single derivative blocks of positive gain. The possibility tha t common factors can appear ''a priori'' in the decomposition of the n umerator polynomial in its real and imaginary parts is considered in t he given synthesis procedure and it is then theoretically solved.