Interval-polynomial stability theory and its applications in testing the strict positive realness of interval transfer functions

Based on value-set geometry and vector operations in the complexplane, this paper improves some early results on the robustD-stability of an interval polynomial. Almost strong Kharitonov-typeresults for some typical stability regions D are presented.Some connections between the critical vertex polynomials withrespect to these stability regions are established. Explicitupper bounds for the number of critical vertex polynomials associatedwith each stability region are derived. We also present a simpledirect procedure for construction of the critical vertex polynomialswith respect to the left-sector stability region. Illustrativeexamples are given. Using the stability theory of interval polynomials,some strong Kharitonov-type results are obtained for strictpositive realness of interval rational functions.