Low order stabilizing controllers for a class of distributed parameter systems

This paper is concerned with reduction of the order of finite-dimensional stabilizing controllers for a class of distributed parameter systems. Since the middle of the 1980s, the design method of finite-dimensional stabilizing controllers of Sakawa type has been generalized for a wider class of parabolic distributed parameter systems with boundary control and/or boundary observation. The controller of Sakawa type consists of two kinds of observers: one is an observer of Luenberger type and the other is an estimator for residual modes. Especially, the latter is called residual mode filter (RMF), and it plays an essential role in the design of finite-dimensional stabilizing controllers when the order of RMF is “sufficiently large”. The purpose of this paper is to propose the design method containing low order RMF. An approach based on stability radius is employed.