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Title: Pointwise Stabilization of a Hybrid System and Optimal Location of Actuator

Abstract

We consider a pointwise stabilization problem for a model arising in the control of noise. We prove that we have exponential stability for the low frequencies but not for the high frequencies. Thus, we give an explicit polynomial decay estimation at high frequencies that is valid for regular initial data while clarifying that the behavior of the constant which intervenes in this estimation there, functions as the frequency of cut. We propose a numerical approximation of the model and study numerically the best location of the actuator at low frequencies.

Authors:
 [1];  [2]
  1. Department of Mathematics, Faculty of Sciences of Monastir (Tunisia), E-mail: kais.ammari@fsm.rnu.tn
  2. Institut de Recherche Mathematique Avancee, Universite Louis Pasteur, 7 rue Rene Descartes (France), E-mail: saidi@math.u-strasbg.fr
Publication Date:
OSTI Identifier:
21067403
Resource Type:
Journal Article
Resource Relation:
Journal Name: Applied Mathematics and Optimization; Journal Volume: 56; Journal Issue: 1; Other Information: DOI: 10.1007/s00245-007-0881-x; Copyright (c) 2007 Springer; www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACTUATORS; APPROXIMATIONS; CONTROL THEORY; HYBRID SYSTEMS; NOISE; POLYNOMIALS; STABILITY; STABILIZATION

Citation Formats

Ammari, Kais, and Saidi, Abdelkader. Pointwise Stabilization of a Hybrid System and Optimal Location of Actuator. United States: N. p., 2007. Web. doi:10.1007/S00245-007-0881-X.
Ammari, Kais, & Saidi, Abdelkader. Pointwise Stabilization of a Hybrid System and Optimal Location of Actuator. United States. doi:10.1007/S00245-007-0881-X.
Ammari, Kais, and Saidi, Abdelkader. Fri . "Pointwise Stabilization of a Hybrid System and Optimal Location of Actuator". United States. doi:10.1007/S00245-007-0881-X.
@article{osti_21067403,
title = {Pointwise Stabilization of a Hybrid System and Optimal Location of Actuator},
author = {Ammari, Kais and Saidi, Abdelkader},
abstractNote = {We consider a pointwise stabilization problem for a model arising in the control of noise. We prove that we have exponential stability for the low frequencies but not for the high frequencies. Thus, we give an explicit polynomial decay estimation at high frequencies that is valid for regular initial data while clarifying that the behavior of the constant which intervenes in this estimation there, functions as the frequency of cut. We propose a numerical approximation of the model and study numerically the best location of the actuator at low frequencies.},
doi = {10.1007/S00245-007-0881-X},
journal = {Applied Mathematics and Optimization},
number = 1,
volume = 56,
place = {United States},
year = {Fri Jun 15 00:00:00 EDT 2007},
month = {Fri Jun 15 00:00:00 EDT 2007}
}
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