Adaptive sampling control of high-gain stabilizable systems

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 exist sim ple adaptation laws for tuning the proportional gain (so-called high-gain a daptive controllers) which do not need to know the system and do not attemp t to identify system parameters. In this paper the authors consider sampled versions of the high-gain adapti ve controller. The motivation for sampling arises from the possibility that the output of a system may not be available continuously, but only at samp led times, The main point of interest is the need to develop techniques for adapting the sampling rate, since the stiffness of the system increases as the proportional gain is increased. Our main result shows that adaptive sa mpling stabilization is possible if the product hk of the decreasing sampli ng interval h and the increasing proportional gain k decreases at a rate pr oportional to 1/log k.