Adaptive high-gain lambda-tracking with variable sampling rate

It is well known that proportional output feedback control can stabilize an y relative-degree one, minimum-phase system if the sign of the feedback is correct and the proportional gain is high enough. Moreover, there exists si mple adaptation laws for tuning the proportional gain (the so-called high-g ain adaptive controllers) which are not based on system identification or p lant parameter estimation algorithms or injection of probing signals. If tr acking of signals is desired, then these simple controllers are also applic able without invoking an internal model if the tracking error is not necess arily supposed to converge to zero but towards a ball around zero of arbitr arily small bur prespecified radius lambda > 0. In this note we consider a sampled version of the high-gain adaptive lambda-tracking controller. The m otivation for sampling arises from the possibility that the output of a sys tem may not be available continuously, but only at discrete time instants. The problem is that the stiffness of the system increases as the proportion al gain is increased. Our result shows that adaptive sampling tracking is p ossible if the product hk of the decreasing sampling rate h and the increas ing proportional gain k decreases at a rare proportional to 1/log k. (C) 19 99 Elsevier Science B.V. All rights reserved.