Stability and strict positive realness of convex polytopes of interval polynomials (Q696267)

Proving the equivalence between assessing the stability of a whole family of matrices or polynomials (a computationally difficult problem) and assessing the stability of the vertices, or at least the edges of the family (a computational tractable problem) has been a cornerstone of robust stability analysis for control systems since the late 1970s and the seminal result of Kharitonov. Kharitonov showed that checking the stability of a whole family of interval polynomials (polynomials whose coefficients belong to independent intervals) is equivalent to checking the stability of only four specific polynomials in the family. The paper focuses on an extension of Kharitonov's theorem to polytopes of interval polynomials, in order to ensure robust stability as well as robust strictly positive realness. Unfortunately, contrary to interval polynomials, it is very unlikely that polytopes of interval polynomials can be used as a physically meaningful model for uncertain dynamical systems. Therefore, the practical relevance of the results obtained here is questionable.