Stabilization of second order evolution equations with unbounded feedback with time-dependent delay

Emilia Fridman; Serge Nicaise; Julie Valein

doi:10.1137/090762105

Stabilization of second order evolution equations with unbounded feedback with time-dependent delay

Emilia Fridman^*, Serge Nicaise, Julie Valein

^*Corresponding author for this work

School of Electrical Engineering

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

60 Scopus citations

Abstract

We consider abstract second order evolution equations with unbounded feedback with time-varying delay. Existence results are obtained under some realistic assumptions. We prove the exponential decay under some conditions by introducing an abstract Lyapunov functional. Our abstract framework is applied to the wave, to the beam, and to the plate equations with boundary delays.

Original language	English
Pages (from-to)	5028-5052
Number of pages	25
Journal	SIAM Journal on Control and Optimization
Volume	48
Issue number	8
DOIs	https://doi.org/10.1137/090762105
State	Published - 2010

Keywords

Lyapunov functional
Second order evolution equations
Stabilization
Time-varying delay
Wave equations

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10.1137/090762105

Cite this

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abstract = "We consider abstract second order evolution equations with unbounded feedback with time-varying delay. Existence results are obtained under some realistic assumptions. We prove the exponential decay under some conditions by introducing an abstract Lyapunov functional. Our abstract framework is applied to the wave, to the beam, and to the plate equations with boundary delays.",

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AB - We consider abstract second order evolution equations with unbounded feedback with time-varying delay. Existence results are obtained under some realistic assumptions. We prove the exponential decay under some conditions by introducing an abstract Lyapunov functional. Our abstract framework is applied to the wave, to the beam, and to the plate equations with boundary delays.

KW - Lyapunov functional

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KW - Stabilization

KW - Time-varying delay

KW - Wave equations

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Stabilization of second order evolution equations with unbounded feedback with time-dependent delay

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