Minimal realisation of bilinear and quadratic input-output difference equations in state-space form

This article studies the realisability property of discrete-time bilinear and quadratic input-output (i/o) equations in the classical state-space form. Constraints on the parameters of the i/o model are suggested that lead to realisable models. Using new formulae for computing basis vectors of certa...

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Bibliographic Details
Published in:International journal of control 2011-12, Vol.84 (12), p.2024-2034
Main Authors: Belikov, J., Kotta, P., Kotta, Ü., Zinober, A.S.I.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
bilinear and quadratic input-output difference equations
Computation
Computer science
control theory
systems
Control theory. Systems
Difference equations
discrete-time systems
Exact sciences and technology
Lists
Mathematical analysis
Mathematical models
Modelling and identification
polynomial method
state-space realisation
Studies
Vector spaces
Vectors (mathematics)
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Summary:This article studies the realisability property of discrete-time bilinear and quadratic input-output (i/o) equations in the classical state-space form. Constraints on the parameters of the i/o model are suggested that lead to realisable models. Using new formulae for computing basis vectors of certain vector spaces of differential one-forms, we present in this article the complete list of the third- and fourth-order realisable i/o bilinear models, and a new realisable subclass of an arbitrary order is suggested. Moreover, we provide the sufficient conditions of the second- and third-order realisable i/o quadratic models, respectively. All the developed theory and algorithms are illustrated by means of several examples.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2011.631587