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Linearizations of affine systems

Linearizations of affine systems We consider three types of nonsingular smooth transformations of nonlinear systems with control. These transformations are induced by changes of variables in the state space and in the control space and by changes of the independent variable. We introduce the notions of integrable and nonintegrable changes of the independent variable (time scalings) and of time-varying orbital linearization. For integrable time scalings, we show that, in a nonlinear time-independent system with control, they diminish its order and that control-independent integrable time scalings reduce affine time-independent systems to affine time-independent systems that cannot be linearized by a feedback. We obtain conditions for local orbital linearization and time-varying orbital linearization of affine time-independent systems with a single control. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Linearizations of affine systems

Differential Equations , Volume 50 (11) – Dec 13, 2014

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References (17)

Publisher
Springer Journals
Copyright
Copyright © 2014 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266114110081
Publisher site
See Article on Publisher Site

Abstract

We consider three types of nonsingular smooth transformations of nonlinear systems with control. These transformations are induced by changes of variables in the state space and in the control space and by changes of the independent variable. We introduce the notions of integrable and nonintegrable changes of the independent variable (time scalings) and of time-varying orbital linearization. For integrable time scalings, we show that, in a nonlinear time-independent system with control, they diminish its order and that control-independent integrable time scalings reduce affine time-independent systems to affine time-independent systems that cannot be linearized by a feedback. We obtain conditions for local orbital linearization and time-varying orbital linearization of affine time-independent systems with a single control.

Journal

Differential EquationsSpringer Journals

Published: Dec 13, 2014

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