Boundary stabilization for a hybrid system of viscoelasticity

Qiong Zhang; Falun Huang

doi:10.1137/S0363012901389913

Boundary stabilization for a hybrid system of viscoelasticity

Qiong Zhang^*, Falun Huang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this paper, we study the boundary feedback stabilization of a hybrid system that is composed of a viscoelastic thin plate with one part of its edge clamped and the remaining free part attached to a viscoelastic rigid body. By adopting the frequency domain method, we prove that the boundary feedback controls together with the dissipation induced by the memory effect are strong enough to secure the result of the exponential stability of energy. We also reach the result of the exponential stability of the hybrid system on the domain with corners without any extra hypotheses on the regularity of solutions.

Original language	English
Pages (from-to)	1643-1660
Number of pages	18
Journal	SIAM Journal on Control and Optimization
Volume	42
Issue number	5
DOIs	https://doi.org/10.1137/S0363012901389913
Publication status	Published - 2003
Externally published	Yes

Keywords

C contraction semigroup
Exponential stability
Hybrid system
Nonsmooth domain
Viscoelasticity

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10.1137/S0363012901389913

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AU - Huang, Falun

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AB - In this paper, we study the boundary feedback stabilization of a hybrid system that is composed of a viscoelastic thin plate with one part of its edge clamped and the remaining free part attached to a viscoelastic rigid body. By adopting the frequency domain method, we prove that the boundary feedback controls together with the dissipation induced by the memory effect are strong enough to secure the result of the exponential stability of energy. We also reach the result of the exponential stability of the hybrid system on the domain with corners without any extra hypotheses on the regularity of solutions.

KW - C contraction semigroup

KW - Exponential stability

KW - Hybrid system

KW - Nonsmooth domain

KW - Viscoelasticity

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Boundary stabilization for a hybrid system of viscoelasticity

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Keywords

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