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Abstract and Applied Analysis
Volume 2013, Article ID 670878, 11 pages
Research Article

Chaos Synchronization Based on Unknown Input Proportional Multiple-Integral Fuzzy Observer

1Laboratory of Modeling, Information & Systems (MIS), University of Picardie Jules Verne (UPJV), 33 rue Saint Leu, 80039 Amiens Cedex 1, France
2Laboratory of Automatic Applied (LAA), M’hamed Bougara University of Boumerdès (UMBB), 35000 Boumerdès, Algeria
3Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway

Received 1 April 2013; Revised 17 June 2013; Accepted 18 June 2013

Academic Editor: Zidong Wang

Copyright © 2013 T. Youssef et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents an unknown input Proportional Multiple-Integral Observer (PIO) for synchronization of chaotic systems based on Takagi-Sugeno (TS) fuzzy chaotic models subject to unmeasurable decision variables and unknown input. In a secure communication configuration, this unknown input is regarded as a message encoded in the chaotic system and recovered by the proposed PIO. Both states and outputs of the fuzzy chaotic models are subject to polynomial unknown input with kth derivative zero. Using Lyapunov stability theory, sufficient design conditions for synchronization are proposed. The PIO gains matrices are obtained by resolving linear matrix inequalities (LMIs) constraints. Simulation results show through two TS fuzzy chaotic models the validity of the proposed method.