Skip to main content
SpringerLink
Log in

Absolute stabilization of singular systems with ferromagnetic hysteresis nonlinearity

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

This paper is concerned with the absolute stabilization problem of a class of singular systems with feedback connected ferromagnetic hysteresis nonlinearities. Firstly, a novel differential-integral loop transformation framework is developed to achieve an augmented singular system model. Secondly, by constructing a new passive output derivative operator of hysteresis nonlinearity and establishing the bound condition of the solution of ferromagnetic hysteresis model, the equivalent absolute stability criterion of singular systems with hysteresis feedback is derived based on KYP method and LMIs technique. Furthermore, the strict LMIs conditions for absolute stabilization are obtained, which can easily be checked by the LMI toolbox in MATLAB. Finally, two examples are given to illustrate the effectiveness of the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Khalil H K. Nonlinear Systems. 3rd ed. New York: Prentice Hall, 2001. 18–280

    Google Scholar 

  2. Brokate M, Sprekels J. Hysteresis and Phase Transitions. New York: Springer-Verlag, 1996. 22–121

    MATH  Google Scholar 

  3. Visintin A. Differential Models of Hysteresis. New York: Springer-Verlag, 1994. 12–265

    MATH  Google Scholar 

  4. Su C Y, Wang Q Q, Chen X K, et al. Adaptive variable structure control of a class of nonlinear system with unknown Prandtl-Ishlinskii hysteresis. IEEE Trans Automat Contr, 2005, 50: 2069–2074

    Article  MathSciNet  Google Scholar 

  5. Oh J H, Bernstein D S. Semilinear Duhem model for rate-independent and rate-dependent hysteresis. IEEE Trans Automat Contr, 2005, 50: 631–645

    Article  MathSciNet  Google Scholar 

  6. Pare T, Hassibi A, How J. A KYP lemma and invariance principle for systems with multiple hysteresis nonlinearities. Int J Control, 2001, 74: 1140–1157

    Article  MathSciNet  MATH  Google Scholar 

  7. Ren B B, Ge S S, Su C Y, et al. Adaptive neural control for a class of uncertain nonlinear systems in pure-feedback form with hysteresis input. IEEE Trans Syst Man Cy-B, 2009, 39: 431–443

    Article  Google Scholar 

  8. Mao J Q, Ding H S. Intelligent modeling and control for nonlinear systems with rate-dependent hysteresis. Sci China Ser F-Inf Sci, 2009, 52: 656–673

    Article  MATH  Google Scholar 

  9. Wei J D, Sun C T. Constructing hysteretic memory in neural networks. IEEE Trans Syst Man Cy-B, 2000, 30: 601–609

    Article  Google Scholar 

  10. Li C T, Tan Y H. Adaptive output feedback control of systems preceded by the Preisach-type hysteresis. IEEE Trans Syst Man Cy-B, 2005, 35: 130–135

    Article  Google Scholar 

  11. Jönsson U. Stability of uncertain systems with hysteresis nonlinearities. Int J Robust Nonli, 1998, 8: 279–293

    Article  MATH  Google Scholar 

  12. Yakubovich V A. The method of matrix inequalities in the theory of stability of nonlinear controlled systems: absolute stability of systems with hysteresis nonlinearities. Automat Rem Contr, 1965, 26: 753–763

    MathSciNet  MATH  Google Scholar 

  13. Krasnoselskii A M, Pokrovskii A V. Dissipativity of a nonresonant pendulum with ferromagnetic friction. Automat Rem Contr, 2006, 67: 221–232

    Article  MathSciNet  Google Scholar 

  14. Gorbet R B, Morris K A, Wang D W L. Passivity-based stability and control of hysteresis in smart actuators. IEEE Trans Contr Syst T, 2001, 9: 5–16

    Article  Google Scholar 

  15. Hodgdon M L. Applications of a theory of ferromagnetic hysteresis. IEEE Trans Magn, 1988, 24: 218–221

    Article  Google Scholar 

  16. Sabir M. Constitutive relations for magneto-mechanical hysteresis in ferromagnetic materials. Int J Eng Sci, 1995, 33: 1233–1249

    Article  MATH  Google Scholar 

  17. Song Z, Zhang H G, Liu D R. An adaptive control method for a class of uncertain nonlinear systems with ferromagnetic hysteresis nonlinearity. In: Proceedings of 27th Chinese Control Conference. Beijing: Beijing University of Aeronautics and Astronautics Press, 2008. 24–28

    Chapter  Google Scholar 

  18. Yang C Y, Zhang Q L, Zhou L N. Strong absolute stability of Lur’e descriptor systems: Popov-type criteria. Int J Robust Nonlin, 2009, 19: 786–806

    Article  MathSciNet  MATH  Google Scholar 

  19. Zhang L Q, Lam J, Xu S Y. On positive realness of descriptor systems. IEEE Trans Circuit S-I, 2002, 49: 401–407

    Article  MathSciNet  Google Scholar 

  20. Yang C Y, Zhang Q L, Lin Y P, et al. Positive realness and absolute stability problem of descriptor systems. IEEE Trans Circuit S-I, 2007, 54: 1142–1149

    Article  MathSciNet  Google Scholar 

  21. Lee L, Chen J L. Strictly positive real lemma and absolute stability for discrete-time descriptor systems. IEEE Trans Circuit S-I, 2003, 50: 788–794

    Article  MathSciNet  Google Scholar 

  22. Lewis F L. A survey of linear singular systems. Circ Syst Signal Pr, 1986, 5: 3–36

    Article  MATH  Google Scholar 

  23. Xu S Y, Lam J. Robust Control and Filtering of Singular Systems. Berlin: Springer-Verlag, 2006. 119-140

  24. Yin G, Zhang J F. Hybrid singular systems of differential equations. Sci China Ser F-Inf Sci, 2002, 45: 241–258

    Article  MathSciNet  MATH  Google Scholar 

  25. Liao X X. Absolute Stability of Nonlinear Control Systems. Beijing: Science Press, 2006. 221–242

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Northeastern University, Shenyang, 110819, China

    HuaGuang Zhang & YingChun Wang

  2. Stake Key Laboratory of Synthetical Automation of Process Industies (Northeasten University), Shenyang, 110004, China

    HuaGuang Zhang & YingChun Wang

  3. Beijing Institute of Spacecraft System Engineering, Beijing, 100094, China

    Zheng Song

Authors
  1. HuaGuang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. YingChun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zheng Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to HuaGuang Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, H., Wang, Y. & Song, Z. Absolute stabilization of singular systems with ferromagnetic hysteresis nonlinearity. Sci. China Inf. Sci. 56, 1–14 (2013). https://doi.org/10.1007/s11432-011-4315-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-011-4315-7

Keywords

Search

Navigation