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 complex plane, this paper improves some early results on the robust D-stability of an interval polynomial. Almost strong Kharitonov-type results for some typical stability regions D are presented. Some connections between the critical vertex polynomials with respect to these stability regions are established. Explicit upper bounds for the number of critical vertex polynomials associated with each stability region are derived. We also present a simple direct procedure for construction of the critical vertex polynomials with respect to the left-sector stability region. Illustrative examples are given. Using the stability theory of interval polynomials, some strong Kharitonov-type results are obtained for strict positive realness of interval rational functions.