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Fractional generalized synchronization in a class of nonlinear fractional order systems

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Abstract

Generalized synchronization in nonlinear fractional order systems occurs whether the states of one system by means of a functional mapping are identical to states of another. This mapping can be obtained if there exists a fractional differential primitive element whose elements are fractional derivatives which generate a differential transcendence basis. In this contribution we investigate the fractional generalized synchronization (FGS) problem for a class of strictly different nonlinear fractional order systems and we consider the master-slave synchronization scheme. As well as, of a natural manner we construct a fractional generalized observability canonical form, we introduce a fractional algebraic observability property, and we design a fractional dynamical controller able to achieve synchronization. These particular forms of FGS are illustrated with numerical results.

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Acknowledgments

Acknowledgments This paper was supported by the Secretaría de Investigación y Posgrado of the Instituto Politécnico Nacional (SIP-IPN) under the research grant 20144056.

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Authors and Affiliations

  1. Departamento de Control Automático, CINVESTAV-IPN, Av. IPN 2508, 07360 , Mexico, Mexico

    Rafael Martínez-Guerra

  2. Instituto Politécnico Nacional, Academia de Mecatrónica, Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Av. IPN 2580, 07340 , Mexico, Mexico

    Juan L. Mata-Machuca

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  1. Rafael Martínez-Guerra
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  2. Juan L. Mata-Machuca
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Correspondence to Juan L. Mata-Machuca.

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Martínez-Guerra, R., Mata-Machuca, J.L. Fractional generalized synchronization in a class of nonlinear fractional order systems. Nonlinear Dyn 77, 1237–1244 (2014). https://doi.org/10.1007/s11071-014-1373-6

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