Femat R. Solis-Perales G.pdf

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Lecture Notes
in Control and Information Sciences
Editors: M. Thoma, M. Morari
378
Ricardo Femat, Gualberto Solis-Perales
Robust Synchronization of
Chaotic Systems via Feedback
ABC
Series Advisory Board
F. Allgöwer, P. Fleming, P. Kokotovic,
A.B. Kurzhanski, H. Kwakernaak,
A. Rantzer, J.N. Tsitsiklis
Authors
Ricardo Femat
IPICYT
Departamento de Matemáticas Aplicadas
Camino a la Presa San José 2055
Col. Lomas 4a. sección
C.P. 78216 San Luis Potosí
México
E-Mail: rfemat@ipicyt.edu.mx
Gualberto Solis-Perales
Universidad de Guadalajara
Centro Universitario de Ciencias Exactas e
Ingenierías
División de Electrónica y Computación
Blvd. Marcelino García
Barragán 1421
Jal. C.P. 44430 Guadalajara
México
E-Mail: gualberto.solis@cucei.udg.mx
ISBN 978-3-540-69306-2
DOI 10.1007/978-3-540-69307-9
Lecture Notes in Control and Information Sciences
Library of Congress Control Number: 2008928642
c
e-ISBN 978-3-540-69307-9
ISSN 0170-8643
2008 Springer-Verlag Berlin Heidelberg
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is
concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting,
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prosecution under the German Copyright Law.
The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply,
even in the absence of a specific statement, that such names are exempt from the relevant protective laws and
regulations and therefore free for general use.
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543210
springer.com
To you, beauty that has shared your time
and all my small conquests
along recent years.
Ricardo Femat
To Saidy, Regina, Estela and Antonio.
Gualberto Solís-Perales
Preface
This pages include the results derived during last ten years about both suppression and
synchronization of chaotic -continuous time- systems. Along this time, our concept
was to study how the intrinsic properties of dynamical systems can be exploited to
suppress and to synchronize the chaotic behavior and what synchronization phenom-
ena can be found under feedback interconnection. Our findings have caused surprise
to us and have stimulated our astonishing capability. Perhaps, reader can imagine our
faces with opens eyes like children seeing around objects; which are possibly obvious
for others and novel for us. A compilation of our surprises about these findings is
being described along this book. Book contains both objectives to share our amaze-
ment and to show our perspective on synchronization of chaotic systems. Thus, while
we were writing the preface, we discussed its scope. Thinking as a book readers, we
found that a preface should answer, in few words, the following question: What can
the reader find in this book?, reader can find our steps toward understanding of cha-
otic behavior and the possibility of suppressing and synchronizing it. We firstly show
the chaos suppression form experimental domain to potential implementation in high
tech system as a levitation system based on High Temperature Superconductors
(HTS). This chapter is used as departing point towards a more complicated problem
the chaotic synchronization. Then, reader travels by the synchronization of the chaotic
behavior world throughout distinct feedback approaches. An extension to classical
feedback is first ste, where a classification of synchronization phenomena and poten-
tial implementation allow to go beyond the control application. Then, a small trip by
geometrical tools to induce synchrony on chaos behavior leads us back to engineering.
Thus, we approach landing onto time-discretization of feedback towards potential
implementation in microcontrollers. Finally, extension on geometrical tools and syn-
chronization are included in last chapter.
April 2008
Ricardo Femat
Gualberto Solís Perales

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