Stabilization of Distributed-Parameter Systems of Parabolic Type and Construction of an Observer

Abstract

This paper deals with the feedback stabilization of distributed-parameter systems of parabolic type and its application to constructing an observer for asymptotic state identification.
It is shown that, when a controller (an observation) can be constructed arbitrarily, observability (controllability) of the system is necessary and sufficient for stabilizing the system so that it has an arbitrarily large damping constant. By applying the results of stabilization, it is possible to construct an observer, the output of which approaches the real state of the system asymptotically with an arbitrary convergence speed.