Some results on feedback stabilization of a one-link flexible arm

The aim of this report is to exhibit a class of stabilizing feedback laws for a structurally undamped one-link flexible arm with control applied at one extremity. A finite-dimensional model of the arm, corresponding to a discretization in space, is first considered. The arm is then modeled by a classical partial differential equation, no finite dimensional approximation being made in the control analysis. In both cases, stability of the closed-loop system is proven, using a Lyapunov method and applying Lasalle's principle. The pratical significance of the proposed results is commented upon and illustrated by simulation experiments.