Stabilization of a rayleigh beam with collocated piezoelectric sensor/actuator

In this paper, stabilization of a Rayleigh beam with collocated piezoelectric sensor/actuator is studied. With a linear output feedback law, several stability results are achieved. The stability of the closed-loop system depends on the location of the actuator. The sufficient and necessary conditions for strong stability are provided. For almost all choices of the ends of the actuator, the energy of the system decreases to zero in a polynomial way and the explicit polynomial decay rate is obtained. Finally, the system is never exponentially stable for any choice of the ends of the actuator.