A method for general design of positive real functions

The objective of this work is to develop a general method for the synthesis of a solution to the problem of designing positive real functions of a prefixed Hurwitz denominator polynomial. Such a synthesis problem is reduced to the calculation of the solution of an equivalent algebraic system of linear equations. The dual problem of designing the denominator polynomial for a prefixed given numerator polynomial is also focused on. The problem is first solved for rational realizable functions and extended in a natural way to nonrational ones by simply addition of single derivative blocks of positive gain. The possibility that common factors can appear "a prior" in the decomposition of the numerator polynomial in its real and imaginary parts is considered in the given synthesis procedure and it is then theoretically solved.