Low-gain adaptive stabilization of infinite-dimensional second-order systems

Abstract

In this paper, low-gain 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 a low-gain adaptive PI controller (proportional plus integral controller). An energy-like function and a multiplier function are introduced and low-gain adaptive stabilization of the linear second-order systems is analyzed.