  It is well known that magnetic energy of the piezoelectric beam is relatively
small, and it does not change the overall dynamics. Therefore, the models,
relying on electrostatic or quasi-static approaches, completely ignore the
magnetic energy stored/produced in the beam. A single piezoelectric beam model
without the magnetic effects is known to be exactly observable and
exponentially stabilizable in the energy space. However, the model with the
magnetic effects is proved to be not exactly observable / exponentially
stabilizable in the energy space for almost all choices of material parameters.
Moreover, even strong stability is not achievable for many values of the
material parameters. In this paper, it is shown that the uncontrolled system is
exactly observable in a space larger than the energy space. Then, by using a
$B^*-$type feedback controller, explicit polynomial decay estimates are
obtained for more regular initial data. Unlike the classical counterparts, this
choice of feedback corresponds to the current flowing through the electrodes,
and it matches better with the physics of the model. The results obtained in
this manuscript have direct implications on the controllability/stabilizability
of smart structures such as elastic beams/plates with piezoelectric patches and
the active constrained layer (ACL) damped beams/plates.
