VIBRATIONAL STABILIZABILITY OF A CLASS OF DISTRIBUTED PARAMETER SYSTEMS.

Stabilization of distributed parameter systems by zero mean parametric perturbations is known to be an alternative stabilization method when feedback and/or feedforward cannot guarantee stability due to the lack of reliable on-line measurements. Conditions of vibrational stabilizability for a class of parabolic partial differential equations (PDE's) are derived and examples of vibrational stabilization of unstable PDE's are presented. The novelty of the approach consists in the fact that all conditions are obtained without resorting to finite dimensional approximations which eliminates the need for truncation error estimates.