Stabilization and finite-gain stabilizability of continuous-time delay linear systems subject to input saturation

Karim Yakoubi (1) , Yacine Chitour (1)

1 L2S - Laboratoire des signaux et systèmes

This paper deals with two problems on stabilization of linear systems by static feedbacks which are bounded and time-delayed, namely global asymptotic stabilization and finite gain L-P-stabilization, p is an element of [1, infinity]. Regarding the first issue, we provide, under standard necessary conditions, two types of solutions for arbitrary small bound on the control and large (constant) delay. The first solution is based on the knowledge of a static stabilizing feedback in the zero-delay case and the second solution is of nested saturation type, which extends results of [2]. For the finite-gain L-P-stabilization issue, we assume that the system is neutrally stable. We show the existence of a linear feedback such that, for arbitrary small bound on the control and large (constant) delay, finite gain L-P-stability holds with respect to every L-P-norm, p is an element of [1, infinity]. Moreover, the corresponding L-P-gain is delay-independent.

Domaines: Mathématiques [math]

Karim Yakoubi, Yacine Chitour. Stabilization and finite-gain stabilizability of continuous-time delay linear systems subject to input saturation. 44th IEEE Conference on Decision Control/European Control Conference (CCD-ECC), Dec 2005, Seville, Spain. ⟨10.1109/cdc.2005.1582960⟩. ⟨hal-02320782⟩