In this paper we study the polynomial stability of a Rayleigh system with distributed delay in dynamic control. After studying the existence and uniqueness of the solution, we showed polynomial stability and finally proved that this polynomial stability is the best that can be had by establishing that there is no exponential stability. Our contribution is the introduction of the distributed delay term in the control.

Rayleigh beam equation, dynamic boundary control, distributed delay, spectral analysis, Rational stabilization.