Compensator Design for Distributed Parameter Systems

Abstract

Stabilization of linear finite dimensional systems is an important design problem in systems control theory and continues to receive much atten tion in the literature. The problem of stabilization of infinite dimensional linear systems is a much harder problem and the results are less complete. While results on state feedback stabilization and observers first appeared as early as 1975, the interest in these problems remained theoretical due to the fact that all observers turned out to be infinite dimensional. Of course what one would really like is a finite dimensional compensator scheme (preferably of low order) which could stabilize a given infinite dimensional system based on finite dimensional observations and inputs. The first result in this direc tion was obtained by Schumacher in 1981 and has since been followed by other finite dimensional compensator schemes which work essentially for the class of distributed systems isolated by Triggiani in 1975 in his fundamental result on feedback stabilization. In this survey an account is given of recent results on stabilization of infinite dimensional systems with the emphasis on implementable compensator schemes.