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.
438-465
Ober, Raimund
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
Montgomery-Smith, Stephen
2be8a832-2542-4fd2-956d-23ed94e1a662
1990
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), .
(doi:10.1137/0328024).
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
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Local EPrints ID: 424997
URI: http://eprints.soton.ac.uk/id/eprint/424997
ISSN: 0363-0129
PURE UUID: 8d8ecc1a-b9a1-4dcd-b9c1-80e31408a78b
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Date deposited: 09 Oct 2018 16:30
Last modified: 16 Mar 2024 04:37
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Author:
Stephen Montgomery-Smith
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