Stabilization of infinite-dimensional undamped second order systems by using a parallel compensator

Abstract

In this paper stabilization of infinite‐dimensional undamped second‐order systems is considered in the case where the input and output operators are collocated. The systems have an infinite number of poles and zeros on the imaginary axis. In the case where only position feedback is available, a parallel compensator is effective. The stabilizer is constructed by a P‐controller for the augmented system which consists of the controlled system and a parallel compensator. The asymptotic stability of the augmented system is proved by LaSalle's invariance principle under compactness of the resolvent.