Equivalence between exponential stabilization and boundary observability for piezoelectric beams with magnetic effect

Abstract

In this paper, we study a one-dimensional dissipative system of piezoelectric beams with magnetic effect, based on the work of Morris and Ozer (in: The proceedings of 52nd IEEE conference on decision & control, pp 3014–3019, 2013). Our main goal is to prove the system’s exponential stability independent of any relation between the coefficients using terms of feedback at the boundary and consequently prove their equivalence with the exact observability at the boundary.