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Nerode equivalence for continuous-time transfer function matrices

Nerode equivalence for continuous-time transfer function matrices
Nerode equivalence for continuous-time transfer function matrices
In this paper we show that a state space realisation in Jordan canonical form for linear multivariable continuous-time systems described by rational transfer function matrices could be obtained in a natural and basic way by using the concept of Nerode equivalence. Both scalar and multivariable cases in the continuous-time setting are discussed. The basic idea of Nerode equivalence is that the state can be identified with a corresponding equivalence class of input. For a linear finite dimensional time-invariant continuous-time system, the zero state is identified with the kernel of certain Hankel operator. This characterisation then led us naturally to the state equations.
nerode equivalence, minimal state space realisation, jordan canonical form, gilbert's diagonal form, interpolation by rational functions, hankel operators
0167-6911
1-20
Liu, Jing
a3428c79-3f08-43ab-9f64-ec895d5e6cba
French, Mark
22958f0e-d779-4999-adf6-2711e2d910f8
Liu, Jing
a3428c79-3f08-43ab-9f64-ec895d5e6cba
French, Mark
22958f0e-d779-4999-adf6-2711e2d910f8

Liu, Jing and French, Mark (2014) Nerode equivalence for continuous-time transfer function matrices. Systems & Control Letters, 1-20. (Submitted)

Record type: Article

Abstract

In this paper we show that a state space realisation in Jordan canonical form for linear multivariable continuous-time systems described by rational transfer function matrices could be obtained in a natural and basic way by using the concept of Nerode equivalence. Both scalar and multivariable cases in the continuous-time setting are discussed. The basic idea of Nerode equivalence is that the state can be identified with a corresponding equivalence class of input. For a linear finite dimensional time-invariant continuous-time system, the zero state is identified with the kernel of certain Hankel operator. This characterisation then led us naturally to the state equations.

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More information

Submitted date: 2014
Keywords: nerode equivalence, minimal state space realisation, jordan canonical form, gilbert's diagonal form, interpolation by rational functions, hankel operators
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 367026
URI: http://eprints.soton.ac.uk/id/eprint/367026
ISSN: 0167-6911
PURE UUID: e1c5b355-d2fb-489b-bd45-b7e3796e27e1

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Date deposited: 22 Jul 2014 08:39
Last modified: 11 Dec 2021 04:40

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Contributors

Author: Jing Liu
Author: Mark French

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