Linearization of discrete-time systems

The algebraic formalism developed in this paper unifies the study of the accessibility problem and various notions of feedback linearizability for discrete-time nonlinear systems. The accessibility problem for nonlinear discrete-time systems is shown to be easy to tackle by means of standard linear...

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Bibliographic Details
Published in:SIAM journal on control and optimization 1996-11, Vol.34 (6), p.1999-2023
Main Authors: ARANDA-BRICAIRE, E, KOTTA, Ü, MOOG, C. H
Format: Article
Language:English
Subjects:
Algebra
Applied mathematics
Applied sciences
Automatic Control Engineering
Computer Science
Computer science
control theory
systems
Control system synthesis
Control theory. Systems
Exact sciences and technology
Modelling and identification
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Summary:The algebraic formalism developed in this paper unifies the study of the accessibility problem and various notions of feedback linearizability for discrete-time nonlinear systems. The accessibility problem for nonlinear discrete-time systems is shown to be easy to tackle by means of standard linear algebraic tools, whereas this is not the case for nonlinear continuous-time systems, in which case the most suitable approach is provided by differential geometry. The feedback linearization problem for discrete-time systems is recasted through the language of differential forms. In the event that a system is not feedback linearizable, the largest feedback linearizable subsystem is characterized within the same formalism using the notion of derived flag of a Pfaffian system. A discrete-time system may be linearizable by dynamic state feedback, though it is not linearizable by static state feedback. Necessary and sufficient conditions are given for the existence of a so-called linearizing output, which in turn is a sufficient condition for dynamic state feedback linearizability.
ISSN:0363-0129
1095-7138
DOI:10.1137/S0363012994267315