Stabilization of a hybrid system of elasticity by feedback boundary damping

Summary A hybrid control system is presented as consisting of an elastic beam linked to a rigid body, and the system is asymptotically stabilized through feedback boundary damping. Solutions of the hybrid system are constructed that decay towards zero at nonexponential, even arbitrarily slow, decay rates. This feedback control analysis complements the authors' earlier report on the open-loop controllability of this same hybrid system, which is a simplified model of a space-structure.This research was partially supported by NSF Grant DMS 86-07687 and AFOSR-ISSA-860088, and the second author also received support from SERC.