TY - GEN
T1 - Exponential stability of a coupled Heat-ODE system
AU - Zhao, Dong Xia
AU - Wang, Jun Min
PY - 2013
Y1 - 2013
N2 - This paper addresses the feedback stabilization of an interconnected Heat-ODE system with the Dirichlet interconnection. The 'interconnection' between the heat equation and the ODE are bi-directional, in which the Dirichlet boundary observation of the heat equation is fed into the ODE, and the velocity of ODE is flowed into the boundary of the heat equation. The semigroup approach is adopted in investigation. By a detailed analysis, we obtain the asymptotic expressions of eigenvalues and eigenfunctions. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. This deduces the spectrum-determined growth condition for the Co-semigroup, and as a consequence, the exponential stability of the system is then followed. Numerical simulations are presented.
AB - This paper addresses the feedback stabilization of an interconnected Heat-ODE system with the Dirichlet interconnection. The 'interconnection' between the heat equation and the ODE are bi-directional, in which the Dirichlet boundary observation of the heat equation is fed into the ODE, and the velocity of ODE is flowed into the boundary of the heat equation. The semigroup approach is adopted in investigation. By a detailed analysis, we obtain the asymptotic expressions of eigenvalues and eigenfunctions. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. This deduces the spectrum-determined growth condition for the Co-semigroup, and as a consequence, the exponential stability of the system is then followed. Numerical simulations are presented.
KW - Dirichlet interconnection
KW - Exponential stability
KW - Heat equation
KW - Riesz basis
UR - http://www.scopus.com/inward/record.url?scp=84882802261&partnerID=8YFLogxK
U2 - 10.1109/CCDC.2013.6560914
DO - 10.1109/CCDC.2013.6560914
M3 - Conference contribution
AN - SCOPUS:84882802261
SN - 9781467355322
T3 - 2013 25th Chinese Control and Decision Conference, CCDC 2013
SP - 169
EP - 172
BT - 2013 25th Chinese Control and Decision Conference, CCDC 2013
T2 - 2013 25th Chinese Control and Decision Conference, CCDC 2013
Y2 - 25 May 2013 through 27 May 2013
ER -