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About the Stabilization of a Nonlinear Perturbed Difference Equation
Author
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-19, 19 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-04-01
Country of Publication
Egypt
No. of Pages
19
Main Subjects
Abstract EN
This paper investigates the local asymptotic stabilization of a very general class of instable autonomous nonlinear difference equations which are subject to perturbed dynamics which can have a different order than that of the nominal difference equation.
In the general case, the controller consists of two combined parts, namely, the feedback nominal controller which stabilizes the nominal (i.e., perturbation-free) difference equation plus an incremental controller which completes the stabilization in the presence of perturbed or unmodeled dynamics in the uncontrolled difference equation.
A stabilization variant consists of using a single controller to stabilize both the nominal difference equation and also the perturbed one under a small-type characterization of the perturbed dynamics.
The study is based on Banach fixed point principle, and it is also valid with slight modification for the stabilization of unstable oscillatory solutions.
American Psychological Association (APA)
de La Sen, Manuel. 2012. About the Stabilization of a Nonlinear Perturbed Difference Equation. Discrete Dynamics in Nature and Society،Vol. 2012, no. 2012, pp.1-19.
https://search.emarefa.net/detail/BIM-463247
Modern Language Association (MLA)
de La Sen, Manuel. About the Stabilization of a Nonlinear Perturbed Difference Equation. Discrete Dynamics in Nature and Society No. 2012 (2012), pp.1-19.
https://search.emarefa.net/detail/BIM-463247
American Medical Association (AMA)
de La Sen, Manuel. About the Stabilization of a Nonlinear Perturbed Difference Equation. Discrete Dynamics in Nature and Society. 2012. Vol. 2012, no. 2012, pp.1-19.
https://search.emarefa.net/detail/BIM-463247
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-463247