Wronskian-based tests for stability of polynomial combinations

Christophe Fonte (1) , Cédric Delattre (1)

1 CRAN - Centre de Recherche en Automatique de Nancy

In this paper, a stability criterion based on counting the real roots of two specific polynomials is formulated. To establish this result, it is shown that a hyperbolicity condition and a strict positivity of a polynomial Wronskian are necessary and sufficient for the stability of any real polynomial. This result is extended to the stability study of some linear combinations of polynomials. Necessary and sufficient conditions of stability are obtained for polynomial segments and planes.

Mots clés: hyperbolic polynomial; Hurwitz polynomial; Hermite-Biehler theorem; uncertain polynomial; Wronskian; Kharitonov polynomials.; Kharitonov polynomials

Domaines: Automatique / Robotique

Christophe Fonte, Cédric Delattre. Wronskian-based tests for stability of polynomial combinations. Systems and Control Letters, 2011, 60 (8), pp.590-595. ⟨10.1016/j.sysconle.2011.04.017⟩. ⟨hal-00597426⟩