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Experimental Synchronization by Means of Observers

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Book cover Synchronization of Integral and Fractional Order Chaotic Systems

Part of the book series: Understanding Complex Systems ((UCS))

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Abstract

In this chapter, we deal with the experimental synchronization of the Colpitts oscillator in real time. Our approach is based on observer design theory in a master–slave configuration. Thus, the chaos synchronization problem can be posed as an observer design procedure, where the coupling signal is viewed as measurable output, and the slave system is regarded as an observer. A polynomial observer is used for synchronizing the Colpitts oscillator employing linear matrix inequalities. Moreover, comparison with a reduced-order observer and a high-gain observer is given to assess the performance of the proposed observer.

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Notes

  1. 1.

    Let us consider the matrix \(\mathbb{A} = \left [a_{i,j}\right ]_{1\leq 1,j\leq n}\), then (see [27])

    $$\displaystyle{ \parallel \mathit{A} \parallel _{\infty }:= n\quad \max _{1\leq i,j\leq n}\vert a_{i,j}\vert }$$

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Authors and Affiliations

  1. Departamento de Control Automatico, CINVESTAV-IPN, Mexico, D.F., Mexico

    Rafael Martínez-Guerra, Claudia A. Pérez-Pinacho & Gian Carlo Gómez-Cortés

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  1. Rafael Martínez-Guerra
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  2. Claudia A. Pérez-Pinacho
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  3. Gian Carlo Gómez-Cortés
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Martínez-Guerra, R., Pérez-Pinacho, C.A., Gómez-Cortés, G.C. (2015). Experimental Synchronization by Means of Observers. In: Synchronization of Integral and Fractional Order Chaotic Systems. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-15284-4_4

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