Advertisement

Input-to-State Stability Analysis of a Class of Interconnected Nonlinear Systems

  • Jia Wang
  • Xiaobei Wu
  • Zhiliang Xu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3930)

Abstract

This paper proposes a new definition of string stability with bounded input from the input-to-state view. By viewing the interconnection as a kind of input to a subsystem, it specifies sufficient conditions of string stability for a class of directed circular interconnected nonlinear systems, which is based on the input-to-state stability analysis and singular perturbation theory. The proof is first conducted on a system with two subsystems, and then expanded to finite N subsystems. Furthermore, directed graph is used as an illustrative tool in this paper.

Keywords

IEEE Transaction Singular Perturbation Interconnected System Singular Perturbation Theory Bounded Input 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ramakrishna, A., Viswanadham, N.: Decentralized control of interconnected dynamical systems. IEEE Transactions on Automatic Control 27, 159–164 (1982)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Siljak, D.D.: Decentralized Control of Complex Systems. Academic Press, Boston (1985)Google Scholar
  3. 3.
    Chen, B.S., Lee, C.H., Chang, Y.C.: Tracking design of uncertain nonlinear SISO systems: adaptive fuzzy approach. IEEE Transactions on Fuzzy Systems 4(1), 32–43 (1996)CrossRefGoogle Scholar
  4. 4.
    Spooner, J.T., Passino, K.M.: Decentralized adaptive control of nonlinear systems using radial basis neural networks. IEEE Transactions on Automatic Control 44(11), 2050–2057 (1999)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Spooner, J.T., Passino, K.M.: Adaptive control of a class of decentralized nonlinear systems. IEEE Transactions on Automatic Control 41(2), 280–284 (1996)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Gavel, D.T., Siljak, D.D.: Decentralized adaptive control: structural conditions for stability. IEEE Transactions on Automatic Control 34(4), 413–426 (1989)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Shi, L., Sigh, S.K.: Decentralized adaptive controller design for large-scale systems with higher order uncertainties. IEEE Transactions on Automatic Control AC-37(8), 1106–1118 (1992)CrossRefGoogle Scholar
  8. 8.
    Jiang, Z.P.: Decentralized and adaptive nonlinear tracking of large-scale systems via output. IEEE Transactions on Automatic control 45(11), 2122–2128 (2000)MATHCrossRefGoogle Scholar
  9. 9.
    Sontag, E.D.: Smooth stability implies coprime factorization. IEEE Transaction on Automatic Control 34(4), 435–443 (1989)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Freeman, R.A.: Global internal stabilizability does not imply global external stabilizability for small sensor disturbances. IEEE Transactions on Automatic Control 40(12), 2119–2122 (1995)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Krstic, M., Li, Z.H.: Inverse optimal design of input-to-state stabilizing nonlinear controllers. IEEE Transactions on Automatic Control 43(3), 336–350 (1998)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Sontag, E.D.: Further facts about input to state stabilization. IEEE Transactions on Automatic Control 35(4), 473–476 (1990)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Sonag, E.D.: On the input-to-state stability property. European Journal of Control 1(1), 24–36 (1995)Google Scholar
  14. 14.
    Jiang, Z.P., Mareels, I.M.Y.: Small-gain control method for nonlinear cascaded systems with dynamic uncertainties. IEEE Transactions on Automatic Control 42(3), 292–308 (1997)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Chu, K.C.: Decentralized control of high speed vehicle string. Transportation Research 8, 361–383 (1974)Google Scholar
  16. 16.
    Chang, S.S.L.: Temporal stability of n-dimensional linear processors and its applications. IEEE Transactions on Circuits and Systems CAS-27(8), 716–719 (1980)MATHCrossRefGoogle Scholar
  17. 17.
    Swaroop, D., Hedrick, J.K.: String stability of interconnection systems. IEEE Trans.on Automatic Control 41(3), 349–357 (1996)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Darbha, S.: A note about the stability of string LTI systems. Journal of Dynamic Systems, Measurement and Control 124(3), 472–475 (2002)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Hedrick, J.K., Tomizuka, M., Varaiya, P.: Control issues in automated highway systems. IEEE Control System Magazine 14(6), 21–32 (1994)CrossRefGoogle Scholar
  20. 20.
    Pant, A., Seiler, P., Hedrick, K.: Mesh stability of look-ahead interconnected systems. IEEE Transactions on Automatic Control 47(2), 403–407 (2002)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Marquez, H.J.: Nonlinear Control Systems Analysis and Design. John Wiley & Sons, Hoboken (2003)MATHGoogle Scholar
  22. 22.
    Kokotovic, P., Hhalil, H.K., O’Reilly, J.: Singular Perturbation Methods in Control: Analysis and Design. Academic, New York (1986)MATHGoogle Scholar
  23. 23.
    Hhalil, H.K.: Nonlilear Systems, 3rd edn. Prentice Hall, Upper Sadle River (2002)Google Scholar
  24. 24.
    Wang, J., Wu, X., Xu, Z.: String Stability of a Class of Interconnected Nonlinear System from the Input to State View. In: 2005 International Conference on Machine learning and Cybernetics (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jia Wang
    • 1
  • Xiaobei Wu
    • 1
  • Zhiliang Xu
    • 1
  1. 1.Department of AutomationNanjing University of Science and TechnologyNanjingP.R.C.

Personalised recommendations