Stabilization of polytopes of plants by their vertices

Christophe Fonte (1) , Houda Meddeb (1) , Michel Zasadzinski (1)

1 CRAN - Centre de Recherche en Automatique de Nancy

This paper aims to assess the stability of a polytope of linear systems by their vertices. These results are based on the Hermite‐Biehler and Edge theorems. A sufficient condition satisfying a constraint on the even (or odd) part of the closed‐loop characteristic polynomials associated with the stabilization of its vertices is proved. Finally, a constructive method to stabilize a polytope of plants with simultaneous and robust linear time‐invariant controllers is established.

Mots clés: polytope of systems; simultaneous stabilization; robust stabilization; common interlacing property

Domaines: Automatique / Robotique

Christophe Fonte, Houda Meddeb, Michel Zasadzinski. Stabilization of polytopes of plants by their vertices. International Journal of Robust and Nonlinear Control, 2019, 29 (18), pp.6398-6418. ⟨10.1002/rnc.4731⟩. ⟨hal-02355289v2⟩