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Bilinear transformation of infinite-dimensional state-space systems and balanced realizations of nonrational transfer functions

Bilinear transformation of infinite-dimensional state-space systems and balanced realizations of nonrational transfer functions
Bilinear transformation of infinite-dimensional state-space systems and balanced realizations of nonrational transfer functions

The bilinear transform maps the open right half plane to the open unit disk and is therefore a suitable tool for carrying over results for continuous-time systems to discrete-time systems and vice versa. Corresponding state-space formulae are widely used and well understood for the case of finite-dimensional systems. In this paper infinite-dimensional generalizations of these formulae are studied for a general class of infinite-dimensional state-space systems. In particular, it is shown that reachability and observability are carried over and that the reachability and observability gramians are preserved under this transformation. Young showed that a wide class of nonrational discrete-time transfer functions admit a balanced state-space representation. It is shown that this result carries over to the continuous-time situation via the bilinear transformation.

0363-0129
438-465
Ober, Raimund
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
Montgomery-Smith, Stephen
2be8a832-2542-4fd2-956d-23ed94e1a662
Ober, Raimund
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
Montgomery-Smith, Stephen
2be8a832-2542-4fd2-956d-23ed94e1a662

Ober, Raimund and Montgomery-Smith, Stephen (1990) Bilinear transformation of infinite-dimensional state-space systems and balanced realizations of nonrational transfer functions. SIAM Journal on Control and Optimization, 28 (2), 438-465. (doi:10.1137/0328024).

Record type: Article

Abstract

The bilinear transform maps the open right half plane to the open unit disk and is therefore a suitable tool for carrying over results for continuous-time systems to discrete-time systems and vice versa. Corresponding state-space formulae are widely used and well understood for the case of finite-dimensional systems. In this paper infinite-dimensional generalizations of these formulae are studied for a general class of infinite-dimensional state-space systems. In particular, it is shown that reachability and observability are carried over and that the reachability and observability gramians are preserved under this transformation. Young showed that a wide class of nonrational discrete-time transfer functions admit a balanced state-space representation. It is shown that this result carries over to the continuous-time situation via the bilinear transformation.

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Published date: 1990

Identifiers

Local EPrints ID: 424997
URI: https://eprints.soton.ac.uk/id/eprint/424997
ISSN: 0363-0129
PURE UUID: 8d8ecc1a-b9a1-4dcd-b9c1-80e31408a78b
ORCID for Raimund Ober: ORCID iD orcid.org/0000-0002-1290-7430

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Date deposited: 09 Oct 2018 16:30
Last modified: 14 Mar 2019 01:21

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Contributors

Author: Raimund Ober ORCID iD
Author: Stephen Montgomery-Smith

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