Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation

Abstract : The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper, we are concerned with a particularly interesting case: Boundary output feedback stabilization of a one-dimensional wave equation system for which the boundary observation suffers from an arbitrary long time delay. We use the observer and predictor to solve the problem: The state is estimated in the time span where the observation is available; and the state is predicted in the time interval where the observation is not available. It is shown that the estimator/predictor based state feedback law stabilizes the delay system asymptotically or exponentially, respectively, relying on the initial data being non-smooth or smooth. Numerical simulations are presented to illustrate the effect of the stabilizing controller.
Keywords : ACL
Type de document :
Article dans une revue
ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2012, 18 (01), pp.22-35. 〈10.1051/cocv/2010044〉
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01917708
Contributeur : Olivier Garrigues <>
Soumis le : vendredi 9 novembre 2018 - 16:00:51
Dernière modification le : jeudi 7 février 2019 - 17:16:48

Lien texte intégral

Identifiants

Collections

Citation

Bao-Zhu Guo, Cheng-Zhong Xu, Hassan Hammouri. Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2012, 18 (01), pp.22-35. 〈10.1051/cocv/2010044〉. 〈hal-01917708〉

Partager

Métriques

Consultations de la notice

23