TY - JOUR
T1 - Boundary feedback stabilization of a Schrödinger equation interconnected with a heat equation
AU - Liu, Junjun
AU - Wang, Junmin
PY - 2013/11
Y1 - 2013/11
N2 - In this paper, we study stabilization for a Schrödinger equation, which is interconnected with a heat equation via boundary coupling. A direct boundary feedback control is adopted. By a detailed spectral analysis, it is found that there are two branches of eigenvalues: one is along the negative real axis, and the other is approaching to a vertical line, which is parallel to the imagine axis. Moreover, it is shown that there is a set of generalized eigenfunctions, which forms a Riesz basis for the energy state space. Finally, the spectrum-determined growth condition is held and the exponential stability of the system is then concluded.
AB - In this paper, we study stabilization for a Schrödinger equation, which is interconnected with a heat equation via boundary coupling. A direct boundary feedback control is adopted. By a detailed spectral analysis, it is found that there are two branches of eigenvalues: one is along the negative real axis, and the other is approaching to a vertical line, which is parallel to the imagine axis. Moreover, it is shown that there is a set of generalized eigenfunctions, which forms a Riesz basis for the energy state space. Finally, the spectrum-determined growth condition is held and the exponential stability of the system is then concluded.
KW - Boundary control
KW - Heat equation
KW - Riesz basis
KW - Schrödinger equation
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=84885754654&partnerID=8YFLogxK
U2 - 10.1007/s11768-013-2199-3
DO - 10.1007/s11768-013-2199-3
M3 - Article
AN - SCOPUS:84885754654
SN - 1672-6340
VL - 11
SP - 558
EP - 562
JO - Journal of Control Theory and Applications
JF - Journal of Control Theory and Applications
IS - 4
ER -