A Retrospective View on Sampled-data { Control Systems

Prelude In this brief article I will attempt to give a fairly personal and retrospective view on the recent developments in the theory of sampled data control systems The emphasis is upon how I came to discover a new function space framework currently called lifting for sampled data systems and how this notion helped to clarify certain issues in the study of such systems It was a fairly cold day in January I was sitting in an old classroom of Kyoto University equipped with a charcoal type heater already obsolete even in those days attending an introductory course on control theory for junior stu dents The professor was teaching us a basic treatment of sampled data systems Figure Here P s describes the correspondence between the incoming and outgoing signals u s and y s of the controlled plant as y s P s u s in terms of Laplace transforms Similarly C z describes those of the controller via z transform to specify its operation in discrete time To interface these two kinds of systems sampling hold operations are introduced The former is