Boundary feedback stabilization of a three-layer sandwich beam

Riesz basis approach

Jun Min Wang, Bao Zhu Guo, Boumediène Chentouf

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

In this paper, we consider the boundary stabilization of a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop system are concluded. Finally, the well-posedness and regularity in the sense of Salamon-Weiss class as well as the exact controllability are also addressed.

Original languageEnglish
Pages (from-to)12-34
Number of pages23
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume12
Issue number1
DOIs
Publication statusPublished - Jan 2006

Fingerprint

Sandwich Beam
Boundary Stabilization
Riesz Basis
Feedback Stabilization
Asymptotic stability
Controllability
Closed loop systems
Eigenvalues and eigenfunctions
Stabilization
Feedback
Exact Controllability
Exponential Stability
Growth Conditions
Well-posedness
Closed-loop System
Eigenfunctions
State Space
Regularity
Class

Keywords

  • Exact controllability
  • Exponential stability
  • Riesz basis
  • Sandwich beam

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Boundary feedback stabilization of a three-layer sandwich beam : Riesz basis approach. / Wang, Jun Min; Guo, Bao Zhu; Chentouf, Boumediène.

In: ESAIM - Control, Optimisation and Calculus of Variations, Vol. 12, No. 1, 01.2006, p. 12-34.

Research output: Contribution to journalArticle

Wang, Jun Min ; Guo, Bao Zhu ; Chentouf, Boumediène. / Boundary feedback stabilization of a three-layer sandwich beam : Riesz basis approach. In: ESAIM - Control, Optimisation and Calculus of Variations. 2006 ; Vol. 12, No. 1. pp. 12-34.
@article{b838889a4f1541d69dfcd4944eeadcee,
title = "Boundary feedback stabilization of a three-layer sandwich beam: Riesz basis approach",
abstract = "In this paper, we consider the boundary stabilization of a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop system are concluded. Finally, the well-posedness and regularity in the sense of Salamon-Weiss class as well as the exact controllability are also addressed.",
keywords = "Exact controllability, Exponential stability, Riesz basis, Sandwich beam",
author = "Wang, {Jun Min} and Guo, {Bao Zhu} and Boumedi{\`e}ne Chentouf",
year = "2006",
month = "1",
doi = "10.1051/cocv:2005030",
language = "English",
volume = "12",
pages = "12--34",
journal = "ESAIM - Control, Optimisation and Calculus of Variations",
issn = "1292-8119",
publisher = "EDP Sciences",
number = "1",

}

TY - JOUR

T1 - Boundary feedback stabilization of a three-layer sandwich beam

T2 - Riesz basis approach

AU - Wang, Jun Min

AU - Guo, Bao Zhu

AU - Chentouf, Boumediène

PY - 2006/1

Y1 - 2006/1

N2 - In this paper, we consider the boundary stabilization of a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop system are concluded. Finally, the well-posedness and regularity in the sense of Salamon-Weiss class as well as the exact controllability are also addressed.

AB - In this paper, we consider the boundary stabilization of a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop system are concluded. Finally, the well-posedness and regularity in the sense of Salamon-Weiss class as well as the exact controllability are also addressed.

KW - Exact controllability

KW - Exponential stability

KW - Riesz basis

KW - Sandwich beam

UR - http://www.scopus.com/inward/record.url?scp=33645769269&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645769269&partnerID=8YFLogxK

U2 - 10.1051/cocv:2005030

DO - 10.1051/cocv:2005030

M3 - Article

VL - 12

SP - 12

EP - 34

JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

SN - 1292-8119

IS - 1

ER -