Adaptive integral control of time-delay systems

It is well known that if the steady-state gain G(0) of a stable lumped system, with transfer function G(s) is positive, then compensating the system by an integral controller k/s, where k is a gain parameter, leads to a stable closed-loop system which achieves tracking of arbitrary constant reference signals, provided that the gain parameter k is positive and sufficiently small. It is also well known that this result extends to certain classes of differential-delay and distributed parameter systems. The authors derive an adaptive version of the above result for the class of stable lumped systems with output delay, i.e. they show that the gain parameter k can be tuned adaptively, so that tracking is achieved for any system of this class. The resulting adaptive tracking controller is not based on system identification or parameter estimation algorithms, nor is the injection of probing signals required