Bernstein Bezout Matrix with Applications to the Generalized Lienard-Chipart Stability Criterion

Abstract

In polynomial and linear control systems, the Lienard-Chipart stability criterion plays an important role in the judgment of the zeros of a real polynomial based on the inertia of a Bezout matrix. In this paper we consider the case in the Bernstein polynomials basis. First, the Bernstein Bezout matrix and some important properties are introduced, and then a generalized perturbations of a real polynomial under the Bernstein polynomials basis is considered. Finally, a generalized Lienard-Chipart stability criterion in terms of the Bernstein Bezout matrix is established.