Extended Kharitonov´s Theorems and their Application

An attempt is made to extend the well-known Kharitonov´s Theorem, which deals with the Hurwitz property of interval polynomials. The extension is carried out in such a manner that the strict Hurwitz property in the original theorem is weakended so that the imaginary axis is incorporated. As a tool for this, the extension is also made for a classical stability criterion, Mikahilov´s Theorem, for which a close look into certain limiting processes is made. As a result of the inspection, several theorems concerning the location of the zeros of interval polynomials are obtained. These results are applied to the robustness problems of positive- realness and strict positive realness for given rational functions with interval coefficients.