Feedback stabilization of bilinear coupled hyperbolic systems

Ilyasse Lamrani; Imad El Harraki; Ali Boutoulout; Fatima-Zahrae El Alaoui

doi:10.3934/dcdss.2020434

Article Contents

2021, Volume 14, Issue 10: 3641-3657. Doi: 10.3934/dcdss.2020434

This issue Previous Article Pata type contractions involving rational expressions with an application to integral equations Next Article Asymptotic behaviors of solution to partial differential equation with Caputo–Hadamard derivative and fractional Laplacian: Hyperbolic case

Feedback stabilization of bilinear coupled hyperbolic systems

1.
TSI Team, Department of Mathematics, Moulay Ismail University, Faculty of Sciences, Meknes, Morocco
2.
Department of Industrial Engineering, National Superior School of Mines, Rabat, Morocco
3.
LERMA, Mohammadia Engineering School, Mohamed V University in Rabat, Morocco
4.
TSI Team, Department of Mathematics, Moulay Ismail University, Faculty of Sciences, Meknes, Morocco

^* Corresponding author: Imad El Harraki
^* Corresponding author: Imad El Harraki

Received: October 31, 2019

Revised: June 30, 2020

Early access: November 2020

Published: October 2021

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Abstract

This paper studies the problem of stabilization of some coupled hyperbolic systems using nonlinear feedback. We give a sufficient condition for exponential stabilization by bilinear feedback control. The specificity of the control used is that it acts on only one equation. The results obtained are illustrated by some examples where a theorem of Mehrenberger has been used for the observability of compactly perturbed systems [18].

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Mathematics Subject Classification: Primary: 93D15, 93D22; Secondary: 93B07.

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