The Rayleigh beam is a perturbation of the Bernoulli–Euler beam. We
establish convergence of the solution of the Exact Controllability Problem
for the Rayleigh beam to the corresponding solution of the Bernoulli–Euler
beam. Convergence is related to a Singular Perturbation Problem. The main
tool in solving this perturbation problem is a weak version of a lower bound
for hyperbolic polynomials.