Stability analysis of piezoelectric beams

Piezoelectric materials are used in many engineering application. When modeling piezoelectric materials the standard assumption is that the electromagnetic field which is used to actuate the piezoelectric material is quasi static. In this paper we show that although the assumption of a quasi static electrical field is valid when one is interested in simulating a piezoelectric material, this assumption renders the system non stabilizable in terms of control. We also show that this issue is caused by the assumption of a quasi static electrical field and therefore can be avoided by modeling a dynamical electrical field.