TY - GEN
T1 - On the stability of an interconnected system of Euler-Bernoulli beam and heat equation with boundary coupling
AU - Krstic, Miroslav
AU - Wang, Jun Min
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=80053154259&partnerID=8YFLogxK
U2 - 10.1109/acc.2011.5990607
DO - 10.1109/acc.2011.5990607
M3 - Conference contribution
AN - SCOPUS:80053154259
SN - 9781457700804
T3 - Proceedings of the American Control Conference
SP - 2356
EP - 2361
BT - Proceedings of the 2011 American Control Conference, ACC 2011
PB - Institute of Electrical and Electronics Engineers Inc.
ER -