<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Fractional-order chaotic unified systems include a variety of fractional-order chaotic systems such as Chen, Lorenz, Lu, Liu, and financial systems. This paper describes a sliding mode controller for synchronisation of fractional-order chaotic unified systems in the presence of uncertainties and external disturbances, and affirms the stability of the controller (which is composed of error dynamics). Moreover, the synchronisation of two separate fractional-order chaotic systems is studied. For this aim, fractional integral sliding surface is defined. Then the sliding mode control rule for stability of error dynamic is presented based on the Lyapunov stability theorem. Simulation results, obtained by using MATLAB, show that the proposed sliding mode has employed an appropriate approach against uncertainties and to reduce the chattering phenomenon that often occurs with sliding mode controllers.</p></abstract>

Fractional-order chaotic unified systems include a variety of fractional-order chaotic systems such as Chen, Lorenz, Lu, Liu, and financial systems. This paper describes a sliding mode controller for synchronisation of fractional-order chaotic unified systems in the presence of uncertainties and external disturbances, and affirms the stability of the controller (which is composed of error dynamics). Moreover, the synchronisation of two separate fractional-order chaotic systems is studied. For this aim, fractional integral sliding surface is defined. Then the sliding mode control rule for stability of error dynamic is presented based on the Lyapunov stability theorem. Simulation results, obtained by using MATLAB, show that the proposed sliding mode has employed an appropriate approach against uncertainties and to reduce the chattering phenomenon that often occurs with sliding mode controllers.

Robust Synchronisation of Uncertain Fractional-Order Chaotic Unified Systems

Proceedings of the Latvian Academy of Sciences. Section B. Natural, Exact, and Applied Sciences.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Robust Synchronisation of Uncertain Fractional-Order Chaotic Unified Systems"}

Fractional-order chaotic unified systems include a variety of fractional-order chaotic systems such as Chen, Lorenz, Lu, Liu, and financial systems. This paper...

Robust Synchronisation of Uncertain Fractional-Order Chaotic Unified Systems

Published Online: Jun 01, 2017

Page range: 69 - 77

Received: Dec 13, 2014

Accepted: Aug 13, 2016

DOI: https://doi.org/10.1515/prolas-2017-0012

Keywords
fractional-order chaotic unified systems, uncertainty, chaos, synchronisation

© by Naeimadeen Noghredani

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Robust Synchronisation of Uncertain Fractional-Order Chaotic Unified Systems

Published Online: Jun 01, 2017

Page range: 69 - 77

Received: Dec 13, 2014

Accepted: Aug 13, 2016

DOI: https://doi.org/10.1515/prolas-2017-0012

Keywordsfractional-order chaotic unified systems, uncertainty, chaos, synchronisation

© by Naeimadeen Noghredani

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
fractional-order chaotic unified systems, uncertainty, chaos, synchronisation