Adaptive H∞ synchronization for uncertain chaotic systems with external disturbance

Choon Ki Ahn; Sung Tae Jung; Sun Kyung Kang; Su Chong Joo

doi:10.1016/j.cnsns.2009.08.009

Adaptive H_∞ synchronization for uncertain chaotic systems with external disturbance

Choon Ki Ahn, Sung Tae Jung, Sun Kyung Kang, Su Chong Joo

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

83 Citations (Scopus)

Abstract

In this paper, we propose a new adaptive H_∞ synchronization scheme for chaotic systems with unknown parameter and external disturbance. Based on Lyapunov stability theory and linear matrix inequality (LMI) approach, the adaptive H_∞ synchronization controller is presented to not only guarantee stable synchronization but also reduce the effect of external disturbance to an H_∞ norm constraint. The proposed controller with adaptive law can be obtained by solving the LMI problem. The adaptive H_∞ synchronization problems for Chua's chaotic system and hyperchaotic Rössler system are presented to show the effectiveness of the proposed chaos synchronization scheme.

Original language	English
Pages (from-to)	2168-2177
Number of pages	10
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	15
Issue number	8
DOIs	https://doi.org/10.1016/j.cnsns.2009.08.009
Publication status	Published - 2010 Aug
Externally published	Yes

Keywords

Adaptive control
Chaotic systems
H Synchronization
Linear matrix inequality (LMI)
Lyapunov stability theory

ASJC Scopus subject areas

Numerical Analysis
Modelling and Simulation
Applied Mathematics

Access to Document

10.1016/j.cnsns.2009.08.009

Cite this

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title = "Adaptive H∞ synchronization for uncertain chaotic systems with external disturbance",

abstract = "In this paper, we propose a new adaptive H∞ synchronization scheme for chaotic systems with unknown parameter and external disturbance. Based on Lyapunov stability theory and linear matrix inequality (LMI) approach, the adaptive H∞ synchronization controller is presented to not only guarantee stable synchronization but also reduce the effect of external disturbance to an H∞ norm constraint. The proposed controller with adaptive law can be obtained by solving the LMI problem. The adaptive H∞ synchronization problems for Chua's chaotic system and hyperchaotic R{\"o}ssler system are presented to show the effectiveness of the proposed chaos synchronization scheme.",

keywords = "Adaptive control, Chaotic systems, H Synchronization, Linear matrix inequality (LMI), Lyapunov stability theory",

author = "Ahn, {Choon Ki} and Jung, {Sung Tae} and Kang, {Sun Kyung} and Joo, {Su Chong}",

note = "Funding Information: This work was supported by the Grant of the Korean Ministry of Education, Science and Technology (The Regional Core Research Program/Center for Healthcare Technology Development).",

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T1 - Adaptive H∞ synchronization for uncertain chaotic systems with external disturbance

AU - Ahn, Choon Ki

AU - Jung, Sung Tae

AU - Kang, Sun Kyung

AU - Joo, Su Chong

N1 - Funding Information: This work was supported by the Grant of the Korean Ministry of Education, Science and Technology (The Regional Core Research Program/Center for Healthcare Technology Development).

PY - 2010/8

Y1 - 2010/8

N2 - In this paper, we propose a new adaptive H∞ synchronization scheme for chaotic systems with unknown parameter and external disturbance. Based on Lyapunov stability theory and linear matrix inequality (LMI) approach, the adaptive H∞ synchronization controller is presented to not only guarantee stable synchronization but also reduce the effect of external disturbance to an H∞ norm constraint. The proposed controller with adaptive law can be obtained by solving the LMI problem. The adaptive H∞ synchronization problems for Chua's chaotic system and hyperchaotic Rössler system are presented to show the effectiveness of the proposed chaos synchronization scheme.

AB - In this paper, we propose a new adaptive H∞ synchronization scheme for chaotic systems with unknown parameter and external disturbance. Based on Lyapunov stability theory and linear matrix inequality (LMI) approach, the adaptive H∞ synchronization controller is presented to not only guarantee stable synchronization but also reduce the effect of external disturbance to an H∞ norm constraint. The proposed controller with adaptive law can be obtained by solving the LMI problem. The adaptive H∞ synchronization problems for Chua's chaotic system and hyperchaotic Rössler system are presented to show the effectiveness of the proposed chaos synchronization scheme.

KW - Adaptive control

KW - Chaotic systems

KW - H Synchronization

KW - Linear matrix inequality (LMI)

KW - Lyapunov stability theory

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