New condition for invariance of ellipsoidal sets for discrete-time saturated systems

Rachid Riah (1) , Mirko Fiacchini (1)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité

In this paper, we consider the problem of characterizingthe invariant and contractive ellipsoids for discrete-timesaturated systems, as an estimate of the domain of attraction.The asymptotic stability of the controlled system is ensured bythe contractive nature of the invariant set. Sufficient conditionsfor the existence of a quadratic set-induced Lyapunov functionare established through the solution of a bilinear matrixinequalities (BMI) problem. Some computational considerationsare analyzed to overcome the problem of complexity. Anillustrative example is given to demonstrate the effectivenessof the proposed results, developed in this paper.

Mots clés: Saturated system; Invariance; Contractivity; Lyapunov function; Convex set

Domaines: Automatique / Robotique; Optimisation et contrôle [math.OC]; Systèmes dynamiques [math.DS]

Rachid Riah, Mirko Fiacchini. New condition for invariance of ellipsoidal sets for discrete-time saturated systems. MSC 2015 - IEEE Multi-Conference on Systems and Control, Sep 2015, Sydney, Australia. ⟨hal-01208092⟩