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L 2 disturbance attenuation for a class of time-delay Hamiltonian systems

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Abstract

This paper considers the problem of L 2-disturbance attenuation for a class of time-delay port-controlled Hamiltonian systems. A γ-dissipative inequality is established by using a proper control law and a storage function. Then based on the Razumikhin stability theorem, a sufficient condition is proposed for the asymptotically stability of the closed-loop system. Finally, the authors investigate the case that there are time-invariant uncertainties belonging to some convex bounded polytypic domain and an L 2 disturbance attenuation control law is proposed. Study of illustrative example with simulation shows that the presented method in this paper works very well in the disturbance attenuation of time-delay Hamiltonian systems.

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References

  1. A. Isidori, Nonlinear Control Systems II, Springer, London, 1999.

    Book  MATH  Google Scholar 

  2. A. J. van der Schaft, L 2-Gain and Passivity Techniques in Nonlinear Control, 2nd ed., Springer-Verlag, Berlin, 2000.

    Google Scholar 

  3. B. M. Maschke and A. J. van der. Schaft, Port-controlled Hamiltonian systems: Modeling origins and system theoretic properties, Proc. of the IFAC Symposium on NOLCOS, Bordeaux, France, 1992.

  4. D. Cheng and Z. Xi, Feedback realization of Hamiltonian systems, Journal of Systems Science & Complexity, 2002, 15(1): 61–68.

    MathSciNet  MATH  Google Scholar 

  5. D. Cheng and Y. Guo, Stabilization of nonlinear systems via the center manifold approach, Systems and Control Letters, 2008, 57(6): 511–518.

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Ortega, A. J. van der. Schaft, B. Maschke, and G. Escobar, Interconnection and damping assignment passitivity-based control of port-controlled Hamiltonian systems, Automatica, 2002, 38(4): 585–596.

    Article  MathSciNet  MATH  Google Scholar 

  7. Y. Wang, D. Cheng, C. Li, and Y. Ge, Dissipative Hamiltonian realization and energy-based L 2 disturbance attenuation control of multimachine power systems, IEEE Trans. Automatic Control, 2003, 48(8): 1428–1433.

    Article  MathSciNet  Google Scholar 

  8. Y. Wang, G. Feng, and D. Cheng, Simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian systems, Automatica, 2007, 43(3): 403–415.

    Article  MathSciNet  MATH  Google Scholar 

  9. Z. Xi, D. Cheng, Q. Lu, and S. Mei, Nonlinear decentralized controller design for multimachine power systems using Hamiltonian function method, Automatica, 2002, 38(3): 527–534.

    Article  MATH  Google Scholar 

  10. Z. Xi and J. Lam, Stabilization of generalized Hamiltonian systems with internally generated energy and applications to power systems, Nonlinear Analysis: Real World Applications, 2008, 9(3): 1202–1223.

    Article  MathSciNet  MATH  Google Scholar 

  11. T. Shen, R. Ortega, Q. Lu, S. Mei, and K. Tamura, Adaptive L 2 disturbance attenuation of Hamiltonian systems with parameter perturbations and application to power systems, Proc. of the 39th IEEE Conf. on Decision and Control, Sydney, Australia, 2000, 5: 4939–4944.

  12. Y. Wang, G. Feng, D. Cheng, and Y. Liu, Adaptive L 2 disturbance attenuation control of multimachine power systems with SMES units, Automatica, 2006, 42(3): 1121–1132.

    Article  MathSciNet  MATH  Google Scholar 

  13. K. Gu, V. L. Kharitonov, and J. Chen, Stability of Time-Delay Systems, Springer-Verlag, Berlin, 2003.

    Book  MATH  Google Scholar 

  14. Z. Lin and H. Fang, On asymptotic stabilizability of linear systems with delayed input, IEEE Trans. Automatic Control, 2007, 52(6): 998–1013.

    Article  MathSciNet  Google Scholar 

  15. F. Mazenc and S. I. Niculescu, Lyapunov stability analysis for nonlinear delay systems, Systems and Control Letters, 2001, 42(4): 245–251.

    Article  MathSciNet  MATH  Google Scholar 

  16. J. Qu and C. Gao, Stability analysis for the large-scale systems with time-delay, Journal of Systems Science & Complexity, 2006, 19(4): 558–565.

    Article  MathSciNet  MATH  Google Scholar 

  17. M. Wu, Y. He, J. She, and G. Liu, Delay-dependent criteria for robust stability of time-varying delay systems, Automatica, 2004, 40(3): 1435–1439.

    Article  MathSciNet  MATH  Google Scholar 

  18. S. Xu, J. Lam, and Y. Zou, New results on delay-dependent robust H∞ control for systems with time-varying delays, Automatica, 2006, 42(2): 343–348.

    Article  MathSciNet  MATH  Google Scholar 

  19. D. Yue, Q. Han, and J. Lam, Network-based robust H∞ control of systems with uncertainty, Automatica, 2005, 41(6): 999–1007.

    Article  MathSciNet  MATH  Google Scholar 

  20. W. Sun and Y. Wang, Stability analysis for time-delay Hamiltonian systems, Int. Conf. on Control, Automation, Robotics and Vision, Singapore, 2006: 475–480.

  21. J. Slotine and W. Li, Applied Nonlinear Control, Prentice-Hall, Englewood Cliffs, NJ, 1991.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Automation, Qufu Normal University, Qufu, 273165, China

    Weiwei Sun

  2. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Yuzhen Wang & Renming Yang

Authors
  1. Weiwei Sun
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  2. Yuzhen Wang
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  3. Renming Yang
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Corresponding author

Correspondence to Weiwei Sun.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant Nos. 61074068, 61004013 and 61034007, the Research Fund the Doctoral Program of Chinese Higher Education under Grant No. 200804220028, China Postdoctoral Science Foundation under Grant No. 20100481300, the Postdoctoral Innovation Program of Shandong Province under Grant No. 200902014, and the Natural Science Foundation of Shandong Province under Grant No. ZR2010FM013.

This paper was recommended for publication by Editor Jifing ZHANG.

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Sun, W., Wang, Y. & Yang, R. L 2 disturbance attenuation for a class of time-delay Hamiltonian systems. J Syst Sci Complex 24, 672–682 (2011). https://doi.org/10.1007/s11424-011-8368-x

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  • DOI: https://doi.org/10.1007/s11424-011-8368-x

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