Adaptive ℋ∞ synchronization of unified chaotic systems

Ju H. Park; D. H. Ji; S. C. Won; S. M. Lee

doi:10.1142/S021798490901934X

Adaptive ℋ_∞ synchronization of unified chaotic systems

Ju H. Park, D. H. Ji, S. C. Won, S. M. Lee

School of Electronics Engineering

Research output: Contribution to journal › Article › peer-review

31 Scopus citations

Abstract

In this paper, the problem of adaptive ℋ_∞ synchronization for unified chaotic systems with unknown parameter and external disturbance is studied. It is noticed that this unified chaotic system contains the noted Lorentz, Lü and Chen systems. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the novel feedback controller with adaptive law is established to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance to an ℋ_∞ norm constraint. A criterion for existence of the controller is given in terms of LMIs. Finally, a numerical example shows the effectiveness of the proposed method.

Original language	English
Pages (from-to)	1157-1169
Number of pages	13
Journal	Modern Physics Letters B
Volume	23
Issue number	9
DOIs	https://doi.org/10.1142/S021798490901934X
State	Published - 10 Apr 2009

Keywords

Adaptive H1 synchronization
Chaotic systems
Dynamic control
LMI.

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abstract = "In this paper, the problem of adaptive ℋ∞ synchronization for unified chaotic systems with unknown parameter and external disturbance is studied. It is noticed that this unified chaotic system contains the noted Lorentz, L{\"u} and Chen systems. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the novel feedback controller with adaptive law is established to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance to an ℋ∞ norm constraint. A criterion for existence of the controller is given in terms of LMIs. Finally, a numerical example shows the effectiveness of the proposed method.",

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AU - Park, Ju H.

AU - Ji, D. H.

AU - Won, S. C.

AU - Lee, S. M.

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Y1 - 2009/4/10

N2 - In this paper, the problem of adaptive ℋ∞ synchronization for unified chaotic systems with unknown parameter and external disturbance is studied. It is noticed that this unified chaotic system contains the noted Lorentz, Lü and Chen systems. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the novel feedback controller with adaptive law is established to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance to an ℋ∞ norm constraint. A criterion for existence of the controller is given in terms of LMIs. Finally, a numerical example shows the effectiveness of the proposed method.

AB - In this paper, the problem of adaptive ℋ∞ synchronization for unified chaotic systems with unknown parameter and external disturbance is studied. It is noticed that this unified chaotic system contains the noted Lorentz, Lü and Chen systems. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the novel feedback controller with adaptive law is established to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance to an ℋ∞ norm constraint. A criterion for existence of the controller is given in terms of LMIs. Finally, a numerical example shows the effectiveness of the proposed method.

KW - Adaptive H1 synchronization

KW - Chaotic systems

KW - Dynamic control

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Adaptive ℋ_∞ synchronization of unified chaotic systems

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Keywords

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