Predictor-based stabilization of finite-dimensional linear autonomous control systems with a constant input delay

Delphine Bresch-Pietri (1) , Christophe Prieur (2) , Emmanuel Trélat (3)

1 GIPSA-SLR - GIPSA - Systèmes linéaires et robustesse
2 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
3 LJLL - Laboratoire Jacques-Louis Lions

We focus on the design of predictor-based feedbacks for finite-dimensional linear autonomous control systems with a constant input delay, with the Artstein reduction approach. This well-known method consists of reducing the delayed control system, by using an integral transform involving the state and the control, to a usual linear system without input delay, on which one can design a stabilizing feedback with usual approaches. In this paper we propose a complete analysis of this approach which is twofold. First of all we invert the Artstein transform and, as a result, we infer a Lyapunov functional for the linear control system with delay. Secondly, we show how the method can be implemented in a simple way.

Domaines: Systèmes et contrôle [cs.SY]

Delphine Bresch-Pietri, Christophe Prieur, Emmanuel Trélat. Predictor-based stabilization of finite-dimensional linear autonomous control systems with a constant input delay. [Research Report] GIPSA-lab. 2015. ⟨hal-01226598v2⟩