On the stability of an interconnected system of Euler-Bernoulli beam and heat equation with boundary coupling

Miroslav Krstic*, Jun Min Wang

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Citations (Scopus)

Abstract

We study the stability of an interconnected system of Euler-Bernoulli beam and heat equation with boundary coupling, where the boundary temperature of the heat equation is fed as the boundary moment of the Euler-Bernoulli beam and, in turn, the boundary angular velocity of the Euler-Bernoulli beam is fed into the boundary heat flux of the heat equation. We show that the spectrum of the closed-loop system consists only of two branches: one along the real axis and the another along two parabolas symmetric to the real axis and open to the imaginary axis. The asymptotic expressions of both eigenvalues and eigenfunctions are obtained. With a careful estimate for the resolvent operator, the completeness of the root subspaces of the system is verified. The Riesz basis property and exponential stability of the system are then proved. Finally we show that the semigroup, generated by the system operator, is of Gevrey class δ > 2.

Original languageEnglish
Title of host publicationProceedings of the 2011 American Control Conference, ACC 2011
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2356-2361
Number of pages6
ISBN (Print)9781457700804
DOIs
Publication statusPublished - 2011

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619

Fingerprint

Dive into the research topics of 'On the stability of an interconnected system of Euler-Bernoulli beam and heat equation with boundary coupling'. Together they form a unique fingerprint.

Cite this