Boundary Feedback Stabilization of a Hybrid System

摘要

The paper deals with boundary feed-back stabilization of an elastic beam which is clamped at one end and linked to a rigid body by the other end. The system is governed by the Euler-Bernoulli beam equation coupled with the Newton-Euler rigid body equation at the boundary. To stabilize the system we consider the boundary moment control and the boundary force control applied on the rigid body. We propose different stabilizing feedback laws and prove exponential stabilization in some cases. Analysis of the asymptotic eigenvalues of the closed-loop systems is carried out together with various numerical simulations. A set of physical parameters is made explicit such that the closed-loop system has non trivial trajectories with some classical feedback law and hence has no asymptotic stability.