Abstract
The control of transverse vibrations of elastic plates of general shape by feedback boundary control is formulated as an abstract evolution equation. Because the control acts locally on the boundary, which possesses a flanged rim with inertial properties of mass and bending moment, the analysis concerns dynamical controllability and stabilizability of a hybrid system. By the approach of energy decay inequalities and Hörmander’s global uniqueness theorem, it is shown that the system is strongly stabilizable by a locally supported damping feedback of boundary velocity and boundary angular velocity, and hence the system is approximately controllable.
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