On Foster’s theorem and positive para odd functions

Abstract

Various tools in the literature are used to enhance the understanding of the Routh-Hurwitz stability theory. Among such tools are Foster’s theorem and positive para odd functions. One of the objectives of this paper is to show strong correlations between these two tools. Such correlations enable us to create simple forms of such functions which can prove useful in tackling stability issues. Also, a simple derivation of Foster’s Theorem is advanced using complex analysis techniques, avoiding the use of circuit network theory which led to Foster’s theorem. A general form of positive and para odd functions is also advanced.