ABSTRACT
In this paper a nonlinear extensible and elastic beam equation with structural damping and Balakrishnan-Taylor damping is considered. The “spillover” problem in stabilization with feedback controllers involving only a finite number of modes is resolved in this paper by an approach of showing the existence of inertial manifolds for the uncontrolled equation. Based upon that existence, a stabilization of the system at a uniform exponential rate is achieved by a linear finite-dimensional feedback control which is robust with respect to the uncertainty of parameters.
