Boundary feedback stabilization of a Schrdinger equation interconnected with a heat equation

作     者：Junjun LIU Junmin WANG 

作者机构：School of MathematicsBeijing Institute of Technology 

出 版 物：《控制理论与应用（英文版）》 (Journal of Control Theory and Applications)

年 卷 期：2013年第11卷第4期

页      面：558-562页

核心收录：

学科分类：0808[工学-电气工程] 07[理学] 070104[理学-应用数学] 0802[工学-机械工程] 0835[工学-软件工程] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation of China(Nos.61074049 61273130) 

主　　题：Schroedinger equation Heat equation Boundary control Stability Riesz basis 

摘      要：In this paper, we study stabilization for a Schoedinger 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.