Polynomial Stability of an Elastic Plate with Dynamical Boundary Control

Yanan Sun; Qiong Zhang

doi:10.1016/j.ifacol.2025.08.096

Polynomial Stability of an Elastic Plate with Dynamical Boundary Control

Yanan Sun
, Qiong Zhang

Beijing Institute of Technology

Research output: Contribution to journal › Conference article › peer-review

Abstract

This work studies the boundary feedback stabilization for an elastic thin plate, where one part of its boundary is clamped and the remaining free part is attached to a rigid body. The boundary feedback controls are applied to the free boundary. Given that the boundary of the domain may have corners, we introduce a proper abstract framework to analyze the well-posedness and estimate the resolvent. When the geometric control condition (GCC) holds, we prove a polynomial energy decay rate of t^-1/2.

Original language	English
Pages (from-to)	232-236
Number of pages	5
Journal	IFAC-PapersOnLine
Volume	59
Issue number	8
DOIs	https://doi.org/10.1016/j.ifacol.2025.08.096
Publication status	Published - 1 Jun 2025
Externally published	Yes
Event	5th Joint IFAC Workshop on Control of Systems Governed by Partial Differential, Equations, CPDE 2025 and Control of Distributed Parameter Systems, CDPS 2025 - Beijing, China Duration: 18 Jun 2025 → 20 Jun 2025

Keywords

C semigroup
elastic plate
polynomial stability

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10.1016/j.ifacol.2025.08.096

Cite this

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title = "Polynomial Stability of an Elastic Plate with Dynamical Boundary Control",

abstract = "This work studies the boundary feedback stabilization for an elastic thin plate, where one part of its boundary is clamped and the remaining free part is attached to a rigid body. The boundary feedback controls are applied to the free boundary. Given that the boundary of the domain may have corners, we introduce a proper abstract framework to analyze the well-posedness and estimate the resolvent. When the geometric control condition (GCC) holds, we prove a polynomial energy decay rate of t-1/2.",

keywords = "C semigroup, elastic plate, polynomial stability",

author = "Yanan Sun and Qiong Zhang",

note = "Publisher Copyright: {\textcopyright} 2025 The Authors.; 5th Joint IFAC Workshop on Control of Systems Governed by Partial Differential, Equations, CPDE 2025 and Control of Distributed Parameter Systems, CDPS 2025 ; Conference date: 18-06-2025 Through 20-06-2025",

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AU - Sun, Yanan

AU - Zhang, Qiong

PY - 2025/6/1

Y1 - 2025/6/1

N2 - This work studies the boundary feedback stabilization for an elastic thin plate, where one part of its boundary is clamped and the remaining free part is attached to a rigid body. The boundary feedback controls are applied to the free boundary. Given that the boundary of the domain may have corners, we introduce a proper abstract framework to analyze the well-posedness and estimate the resolvent. When the geometric control condition (GCC) holds, we prove a polynomial energy decay rate of t-1/2.

AB - This work studies the boundary feedback stabilization for an elastic thin plate, where one part of its boundary is clamped and the remaining free part is attached to a rigid body. The boundary feedback controls are applied to the free boundary. Given that the boundary of the domain may have corners, we introduce a proper abstract framework to analyze the well-posedness and estimate the resolvent. When the geometric control condition (GCC) holds, we prove a polynomial energy decay rate of t-1/2.

KW - C semigroup

KW - elastic plate

KW - polynomial stability

UR - https://www.scopus.com/pages/publications/105022713553

U2 - 10.1016/j.ifacol.2025.08.096

DO - 10.1016/j.ifacol.2025.08.096

M3 - Conference article

AN - SCOPUS:105022713553

SN - 2405-8963

VL - 59

SP - 232

EP - 236

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 8

T2 - 5th Joint IFAC Workshop on Control of Systems Governed by Partial Differential, Equations, CPDE 2025 and Control of Distributed Parameter Systems, CDPS 2025

Y2 - 18 June 2025 through 20 June 2025

ER -

Polynomial Stability of an Elastic Plate with Dynamical Boundary Control

Abstract

Keywords

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