Stability Analysis of Piezoelastic Structures for Robust Vibration Control

The design of an observer for self sensing actuation of functional materials requires acurate modeling of the piezoelastic structure under investigation. Under the assumption of linear piezoelasticity and Kirchhoff plate theory, the resulting mathematical structure facilitates controller design for harmonic disturbance suppression. Stability issues of the infinite dimensional model are resolved in a straightforward manner by application of results on positive real transfer functions in conjunction with the small gain theorem. If the disturbance frequency is unknown, the proposed controller can be extended by an ordinary differential equation for the unknown frequency which is derived using a stability argument involving the Hamilton-Jacobi inequality.