Continuous state representations for AR Systems

Heide Glüsing-Lüerßen

doi:10.1007/BF01212368

Continuous state representations for AR Systems

Heide Glüsing-Lüerßen

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this paper we consider in a behavioral setting the subclass of dis-crete-time, linear, finite-dimensional systems, which can be represented by autoregressive (AR) equations. It will be shown that, with respect to the convergence of all coefficients in an AR representation, there exist continuously dependent input-state-output (i/s/o) representations, under the condition that some specified degree remains constant. This continuous i/s/o representation is given by the Fuhrmann realization.

Original language	English
Pages (from-to)	82-95
Number of pages	14
Journal	Mathematics of Control, Signals, and Systems
Volume	8
Issue number	1
DOIs	https://doi.org/10.1007/BF01212368
State	Published - Mar 1995

Keywords

Continuity of systems
Linear systems
Polynomial matrix representations
Realization theory

ASJC Scopus subject areas

Control and Systems Engineering
Signal Processing
Control and Optimization
Applied Mathematics

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10.1007/BF01212368

Cite this

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abstract = "In this paper we consider in a behavioral setting the subclass of dis-crete-time, linear, finite-dimensional systems, which can be represented by autoregressive (AR) equations. It will be shown that, with respect to the convergence of all coefficients in an AR representation, there exist continuously dependent input-state-output (i/s/o) representations, under the condition that some specified degree remains constant. This continuous i/s/o representation is given by the Fuhrmann realization.",

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AB - In this paper we consider in a behavioral setting the subclass of dis-crete-time, linear, finite-dimensional systems, which can be represented by autoregressive (AR) equations. It will be shown that, with respect to the convergence of all coefficients in an AR representation, there exist continuously dependent input-state-output (i/s/o) representations, under the condition that some specified degree remains constant. This continuous i/s/o representation is given by the Fuhrmann realization.

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KW - Linear systems

KW - Polynomial matrix representations

KW - Realization theory

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Continuous state representations for AR Systems

Abstract

Keywords

ASJC Scopus subject areas

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