Stability criteria for bilinear systems with delayed state and saturating actuators

Silviu-Iulian Niculescu (1) , Sophie Tarbouriech (2) , Jean-Michel Dion (3) , Luc Dugard (1)

1 LAG - Laboratoire d'automatique de Grenoble
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
3 TIMC-IMAG - Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble - UMR 5525

In this paper, the problem of the closed-loop stability of a class of bilinear systems with delayed state and saturating actuators is considered. Delay-independent sufficient conditions for the uniform asymptotic stability of the closed-loop system via a memoryless static state feedback are developed. The closed-loop stability conditions and the corresponding memoryless control laws are expressed in terms of symmetric positive definite solutions of appropriate finite dimensional algebraic Riccati equations.

Mots clés: Actuators; Asymptotic stability; Closed loop control systems; Control theory; Differential equations; Lyapunov methods; Matrix algebra; Riccati equations; Stability criteria; Bilinear systems; Closed loop stability conditions; Euclidean space; Lyapunov Krasovskii technique; Memoryless control law; Delay control systems

Domaines: Automatique / Robotique

Silviu-Iulian Niculescu, Sophie Tarbouriech, Jean-Michel Dion, Luc Dugard. Stability criteria for bilinear systems with delayed state and saturating actuators. 34th IEEE Conference on Decision and Control (CDC'95), Dec 1995, New Orleans, United States. pp.2064-2069. ⟨hal-02301665⟩