Abstract
In this paper, we study the well-posedness and exact controllability of a system described by a fourth order Schrodinger equation on a bounded domain of ${\mathbb R}^{n}(n\geqslant 2)$ with boundary control and collocated observation. The Neumann boundary control problem is first discussed. It is shown that the system is well-posed in the sense of D. Salamon. This implies the exponential stability of the closed-loop system under proportional output feedback control. The well-posedness result is then generalized to the Dirichlet boundary control problem. In particular, in order to conclude feedback stabilization from well-posedness, we discuss the exact controllability with the Dirichlet boundary control, which is similar to the Neumann boundary control case. In addition, we show that both systems are regular in the sense of G. Weiss and their feedthrough operators are zero.
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