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Anticipating synchronization of chaotic Lur'e systems
Henri Huijberts1, Henk Nijmeijer, Toshiki Oguchi
1School of Engineering and Materials Science, Queen Mary, University of London, Mile End Road, London E1 4NS, United Kingdom.
Chaos (Woodbury, N.Y.)
|April 7, 2007
Summary
This study explores anticipating synchronization in chaotic time-delayed Lur
Area of Science:
- Nonlinear Dynamics
- Control Theory
- Chaos Theory
Background:
- Chaotic systems with time delays are prevalent in various scientific and engineering fields.
- Understanding and controlling synchronization phenomena in these systems is crucial for applications.
- Lur'e-type systems represent a significant class of nonlinear systems with time delays.
Purpose of the Study:
- To investigate anticipating synchronization in chaotic time-delayed Lur'e-type systems.
- To establish conditions for achieving anticipating synchronization in a master-slave configuration.
- To demonstrate the practical applicability of the proposed methods.
Main Methods:
- Development of three distinct scenarios for achieving anticipating synchronization.
- Formulation of sufficient conditions for the existence of synchronizing slave systems.
- Utilization of linear matrix inequalities (LMIs) for deriving these conditions.
Main Results:
- Sufficient conditions for anticipating synchronization are derived using LMIs.
- The effectiveness of the proposed methods is validated through simulations.
- Successful synchronization is demonstrated on specific chaotic systems.
Conclusions:
- The study provides a robust framework for achieving anticipating synchronization in complex systems.
- The derived LMI conditions offer a practical approach for designing synchronizing controllers.
- The findings are applicable to time-delayed chaotic systems like the Rossler and Chua oscillators.
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