Journal of Zhejiang University-SCIENCE A

, Volume 7, Supplement 2, pp 223–227 | Cite as

Passive control of a class of chaotic dynamical systems with nonlinear observer

  • Qi Dong-lian 
  • Song Yun-zhong 


A passive control strategy with nonlinear observer is proposed, which can be used to control a class of chaotic dynamical systems to stabilize at different equilibrium points. If the nonlinear function of chaotic system satisfies Lipschitz condition, the nonlinear observer can observe the state variables of the chaotic systems. An important property of passive system is studied to control chaotic systems, that is passive system can be asymptotically stabilized by state feedback controller whose state variables are presented by nonlinear observer. Simulation results indicated that the proposed chaos control method is very effective in a class of chaotic systems.

Key words

Chaotic dynamical system Passive theory Nonlinear observer 

CLC number



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  1. Byrnes, C.I., Isidori, A., 1991. Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear system. IEEE Trans. Automat. Contr., 36(11):1228–1240. [doi:10.1109/9.100932]MathSciNetCrossRefMATHGoogle Scholar
  2. Chen, G., Chen, G.R., 1999. Feedback control of unknown chaotic dynamical systems based on time-series data. IEEE Trans. Circu. Sys., 46(5):640–644. [doi:10.1109/81.762931]MathSciNetCrossRefMATHGoogle Scholar
  3. Femat, R., Alvarez-Ramirez, J., 1997. Synchronization of a class of strictly different chaotic oscillators. Physics Letters A, 236(4):307–313. [doi:10.1016/S0375-9601(97)00786-X]MathSciNetCrossRefMATHGoogle Scholar
  4. Hill, D., Moylan, P., 1976. The stability of nonlinear dissipative system. IEEE Trans. Automat. Contr., 21(5):708–711. [doi:10.1109/TAC.1976.1101352]MathSciNetCrossRefMATHGoogle Scholar
  5. Li, G.F., Li, H.Y., Yang, C.W., 2005. Observer-based passive control for uncertain linear systems wiin delay in state and control input. Chinese Physics, 14(12):2379–2386. [doi:10.1088/1009-1963/14/12/001]CrossRefGoogle Scholar
  6. Lorenz, E.N., 1963. Deterministic non-periodic flows. J. Atmos. Sci., 20(2):130–141. [doi:10.1175/1520-0469(1963)020〈0130:DNF〉2.0.CO;2]CrossRefGoogle Scholar
  7. Nam, H.J., Juwha, J., Jin, H.S., 1997. Generalized Luenberger-like Observer for Nonlinear Systems. Proceeding of the American Control Conference, p.2180–2183.Google Scholar
  8. Qi, D.L., Li, X.R., Zhao, G.Z., 2004. Passive control of hybrid chaotic dynamical systems. Journal of Zhejiang University (Engineering Science), 38(1):86–89 (in Chinese).Google Scholar
  9. Qi, D.L., Wang, J.J., Zhao, G.Z., 2005. Passive control of permanent magnet synchronous motor chaotic system. Journal of Zhejiang University SCIENCE, 6A(7):728–732. [doi:10.1631/jzus.2005.A0728]CrossRefGoogle Scholar
  10. Ott, E., Grebogi, C., York, J.A., 1990. Controlling chaos. Phys. Rev. Lett., 64(11):1196–1199. [doi:10.1103/PhysRevLett.64.1196]MathSciNetCrossRefMATHGoogle Scholar
  11. Wen, Y., 1999. Passive equivalence of chaos in Lorenz system. IEEE Transaction on Circuits and Systems—I: Fundamental Theory and Application, 46(7):876–878. [doi:10.1109/81.774240]CrossRefGoogle Scholar
  12. Yang, L., Liu, Z., 1998. An improvement and proof of OGY method. Appl. Math. and Mech., 19(1):1–8.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Zhejiang University 2006

Authors and Affiliations

  • Qi Dong-lian 
    • 1
  • Song Yun-zhong 
    • 1
    • 2
  1. 1.School of Electrical EngineeringZhejiang UniversityHangzhouChina
  2. 2.Department of Electrical EngineeringHenan Polytechnic UniversityJiaozuoChina

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