The control of dist,ributed parameter (DP) systems represents a real challenge, both from a theoretical and a practical point of view, to the systems engineer. Distribut.ed parameter systems arise in various application areas, such as chemical proms systems, aerospace systems, magneto-hydrodynamic systems, and communicat. ions systems, to ment.ion just a few. Thus, there is sufficient motivation for research directed t,oward the analysis, synt.hesis, and design techniques for DP systems. On t.he surface, it. may appear that t.he available theory for distributed parameter systems is almost at the same level as that associated with lumped systems. However, there exists a much wider gap between the theory and its applications. In the remainder of this correspondence, we shall briefly discus the reasons for this gap and suggest, certain tentative approaches which may contribute to the development of a theory and computat,ional algorithms which take into account. some of the practical problems associated with the design of controllers for DP systems. In order to make these concepts clear it. becomes necessary to briefly review, in an informal manner, what a DP system is and in what sense it differs, from both a mat,hemat.ical and a practical point of view, from a conventional lumped system.