Low-gain adaptive stabilization of infinite-dimensional second-order systems (Q1856952)

The paper is devoted to the study of the low-gain adaptive stabilization of infinite-dimensional undamped second-order systems with unbounded input and output operators which are asymptotically stabilized by some scalar output feedback. The adaptive stabilizer is constructed by a low-gain adaptive PI controller (proportional plus integral controller). An energy-like (Lyapunov-like) function and a multiplier function are introduced. It is shown that the existence of these functions satisfying suitable hypotheses is fundamental to stabilize second-order systems. The author gives an example related to a linear undamped elastic string system.