Stabilization of infinite-dimensional second-order systems by adaptive PI-controllers

In this paper adaptive 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. The adaptive stabilizer is constructed by an adaptive PI-controller (proportional plus integral controller). An energy-like function and a multiplier function are introduced and adaptive stabilization of the linear second-order systems is analyzed. Copyright (C) 2001 John Wiley & Sons, Ltd.