Dabbene, Fabrizio (Pol. di Torino), Polyak, Boris (Russian Acad. of Sciences), Tempo, Roberto (Pol. di Torino)

On the Complete Instability of Interval Polynomials

Scheduled for presentation during the Mini-Symposium "Randomized and Probabilistic Techniques for Complex Systems Design" (MoP08), Monday, July 24, 2006, 17:25−17:50, Room I

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 20, 2024

Abstract

In this paper, we consider an interval polynomial p(s,k) with coefficients varying in given intervals. The celebrated Theorem of Kharitonov states that p(s,k) is Hurwitz if and only if four specific vertex polynomials are Hurwitz. We turn our attention to the design counterpart of this result. In particular, we pose the following question: Is the interval polynomial completely unstable or there exists at least one Hurwitz polynomial in the family p(s,k)? If the answer to this question is affirmative, then the objective is to find such a Hurwitz polynomial. Following previous research on mixed methods for fixed order controller design, we propose a mixed deterministic/randomized approach to solve this problem.