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An LMI approach to robust synchronization of a class of chaotic systems with gain variations

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  • Asheghan, Mohammad Mostafa
  • Beheshti, Mohammad T.H.

Abstract

This paper presents a novel approach to robust chaos synchronization by linear-state-feedback controller for a class of uncertain chaotic systems with parameters perturbation, different external disturbances and gain variation on both master system and slave system. Based on the Lyapunov stability theory, a sufficient condition is then proposed in Theorem 1. It is shown that chaos synchronization can be achieved at an exponential convergence rate, when synchronization error will be bounded, as a result of noise presence. Applying Schur complement and some matrix manipulation techniques, the results are then transformed into the linear matrix inequality (LMI) form and are presented in Theorem 2. Error bound is minimized through LMI minimization techniques as given in Theorem 3. Finally, the effectiveness of theorems proposed herein is verified demonstrated by the chaotic Murali–Lakshmanan–Chua system.

Suggested Citation

  • Asheghan, Mohammad Mostafa & Beheshti, Mohammad T.H., 2009. "An LMI approach to robust synchronization of a class of chaotic systems with gain variations," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1106-1111.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:2:p:1106-1111
    DOI: 10.1016/j.chaos.2009.03.152
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    References listed on IDEAS

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    1. Behzad, Mehdi & Salarieh, Hassan & Alasty, Aria, 2008. "Chaos synchronization in noisy environment using nonlinear filtering and sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1295-1304.
    2. Jiang, Guo-Ping & Zheng, Wei Xing, 2005. "An LMI criterion for linear-state-feedback based chaos synchronization of a class of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 437-443.
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