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Nonlinear Dynamics

, Volume 80, Issue 1–2, pp 221–226 | Cite as

A new stability result for nonlinear cascade time-delay system and its application in chaos control

  • Hua Wang
  • Jiu-Peng Wu
  • Xiao-Shu Sheng
  • Xin Wang
  • Peng Zan
Original Paper

Abstract

Based on the converse Lyapunov stability theorem and invariant set theory, this paper presents a new theorem for the nonlinear cascade delay system. With this new proposed method, a lot of coupled items can be taken as zero items. So the whole system can be converted to a very simple form. Also, a simple chaos control technique is proposed for the uncertain time-delay Lorenz chaotic system via this new method. The controller designed is linear and easy to be implemented. Simulation results for uncertain chaotic systems are provided to illustrate the effectiveness of the proposed scheme.

Keywords

Cascade delay system Zero items Delay chaotic system Linear controller 

Notes

Acknowledgments

The authors would thank Professor Stefan Siegmund for his useful suggestions in the proof of Theorem 1.

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Hua Wang
    • 1
  • Jiu-Peng Wu
    • 1
  • Xiao-Shu Sheng
    • 1
  • Xin Wang
    • 1
  • Peng Zan
    • 1
  1. 1.Shanghai Key Laboratory of Power Station Automation Technology, School of Mechatronics Engineering and AutomationShanghai UniversityShanghaiChina

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