Copositive Conditions for LMI-Based Controller and Observer Design

Juan Carlos Arceo Luzanilla (1) , Jimmy Lauber (1)

1 LAMIH - Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201

In this report we illustrate that nonlinear control and observer design can be described as a Positivstellensatz problem, we consider a quadratic candidate function to stabilize nonlinear systems that have been modeled via the nonlinear sector methodology as an exact convex representation. New shape-independent conditions for satisfying positiveness in double sums are established based on the concept of copositivity. The conditions obtained are compared with previous approaches found in the literature via a numerical example.

Mots clés: Copositive; Exact Convex Representations; Linear Matrix Inequalities (LMIs); Nonlinear Sector; Fuzzy Systems; Relaxed Conditions; Takagi-Sugeno

Domaines: Automatique / Robotique

Juan Carlos Arceo Luzanilla, Jimmy Lauber. Copositive Conditions for LMI-Based Controller and Observer Design. 21st IFAC World Congress, Jul 2020, Berlin, Germany. pp.7959-7964, ⟨10.1016/j.ifacol.2020.12.2195⟩. ⟨hal-03406734⟩