On stabilizability and sampling for infinite dimensional systems

Author

Rosen, I.G. ; Wang, C.

Author_Institution

Dept. of Math., Univ. of Southern California, Los Angeles, CA, USA

Volume

37

Issue

10

fYear

1992

fDate

10/1/1992 12:00:00 AM

Firstpage

1653

Lastpage

1656

Abstract

Some questions, either motivated by or related to time sampling, regarding the stabilizability of infinite-dimensional or distributed parameter systems are considered. In particular, these include the characteristics of those systems which are finite rank stabilizable, and the preservation of stabilizability under sampling. A pathological class of systems, which, when sampled, may be rendered unstabilizable by arbitrarily small perturbations in the sampling rate, is identified. The approach taken in establishing these results is based upon a spectral decomposition of the infinitesimal generator of the underlying open-loop semigroup. The results obtained apply to control systems with dynamics described by broad classes of partial and functional differential equations that arise frequently in applications

Keywords

distributed parameter systems; multidimensional systems; sampled data systems; spectral analysis; stability; distributed parameter systems; dynamics; functional differential equations; infinite dimensional systems; infinitesimal generator; open-loop semigroup; partial differential equations; sampling; sampling rate; spectral decomposition; stability; stabilizability; Control systems; Differential equations; Distributed parameter systems; Hilbert space; Mathematics; Open loop systems; Optimal control; Pathology; Riccati equations; Sampling methods;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.256405

Filename

256405