Feedback control of second-order evolution equations with unbounded observation†

Abstract

Feedback control is developed for a class of distributed systems described by second-order evolution equations with unbounded observation. In order to increase the degree of stability of the system, a dynamic compensator is designed on the basis of a finite-dimensional model of the system, and a feedback control system is constructed by using sensor outputs. It is shown that the degree of stability of the whole system including the compensator is improved by ‘modal control’ based on a finite-dimensional modal model.