Ruili Wen, Shugen Chai
Abstract:
We consider an open-loop system of a fourth order Schrodinger equation
with variable coefficients and Neumann boundary control and collocated
observation. Using the multiplier method on Riemannian manifold we show that
that the system is well-posed in the sense of Salamon.
This implies that the exponential stability of the closed-loop system under
the direct proportional output feedback control and the exact controllability
of open-loop system are equivalent. So in order to conclude feedback
stabilization from well-posedness, we study the exact controllability under
a uniqueness assumption by presenting the observability inequality for the
dual system. In addition, we show that the system is regular in the sense
of Weiss, and that the feedthrough operator is zero.
Submitted May 25, 2016. Published August 12, 2016.
Math Subject Classifications: 93C20, 35L35, 35B37.
Key Words: Fourth order Schrodinger equation; variable coefficients;
well-posedness; exact controllability; boundary control;
boundary observation.
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Ruili Wen School of Mathematical Sciences Shanxi University, Taiyuan 030006, China email: wenruili@sxu.edu.cn | |
Shugen Chai School of Mathematical Sciences Shanxi University, Taiyuan 030006, China email: sgchai@sxu.edu.cn |
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