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Analysis and control for a new chaotic system via piecewise linear feedback

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  • Zhang, Jianxiong
  • Tang, Wansheng

Abstract

This paper presents a new three-dimensional chaotic system containing two system parameters and a nonlinear term in the form of arc-hyperbolic sine function. The complicated dynamics are studied by virtue of theoretical analysis, numerical simulation and Lyapunov exponents spectrum. The system proposed is converted to an uncertain piecewise linear system. Then, based on piecewise quadratic Lyapunov function technique, the global control of the new chaotic system with α-stability constraint via piecewise linear state feedback is studied, where the optimal controller maximizing the decay rate α can be obtained by solving an optimization problem under bilinear matrix inequalities (BMIs) constraints.

Suggested Citation

  • Zhang, Jianxiong & Tang, Wansheng, 2009. "Analysis and control for a new chaotic system via piecewise linear feedback," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2181-2190.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:4:p:2181-2190
    DOI: 10.1016/j.chaos.2009.03.158
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    References listed on IDEAS

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    1. Nazzal, Jamal M. & Natsheh, Ammar N., 2007. "Chaos control using sliding-mode theory," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 695-702.
    2. Sun, Huijing & Cao, Hongjun, 2008. "Chaos control and synchronization of a modified chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1442-1455.
    3. Niu, Ben & Wei, Junjie, 2008. "Stability and bifurcation analysis in an amplitude equation with delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1362-1371.
    4. Qi, Guoyuan & Chen, Guanrong & Du, Shengzhi & Chen, Zengqiang & Yuan, Zhuzhi, 2005. "Analysis of a new chaotic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(2), pages 295-308.
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