Abstract
Generalized synchronization for nonlinear fractional-order systems occurs when the states of one system are identical to states of another by means of a functional mapping. This mapping can be obtained if there exists a fractional differential primitive element, whose elements are fractional derivatives that generate a differential transcendence basis. In this chapter, we investigate the fractional generalized synchronization (FGS) problem for strictly different nonlinear fractional-order systems, and we consider the master–slave synchronization scheme. Moreover, we construct in a natural manner a fractional generalized observability canonical form (FGOCF), and we introduce a fractional algebraic observability (FAO) 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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Martínez-Guerra, R., Pérez-Pinacho, C.A., Gómez-Cortés, G.C. (2015). Fractional Generalized Synchronization in Nonlinear Fractional-Order Systems via Dynamical Feedback. In: Synchronization of Integral and Fractional Order Chaotic Systems. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-15284-4_13
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DOI: https://doi.org/10.1007/978-3-319-15284-4_13
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