Input-to-State Stability Analysis of a Class of Interconnected Nonlinear Systems | SpringerLink
Skip to main content
Springer Nature Link
Log in

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

  • Conference paper
Advances in Machine Learning and Cybernetics

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3930))

  • 1318 Accesses

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.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Ramakrishna, A., Viswanadham, N.: Decentralized control of interconnected dynamical systems. IEEE Transactions on Automatic Control 27, 159–164 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  2. Siljak, D.D.: Decentralized Control of Complex Systems. Academic Press, Boston (1985)

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  6. Gavel, D.T., Siljak, D.D.: Decentralized adaptive control: structural conditions for stability. IEEE Transactions on Automatic Control 34(4), 413–426 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  9. Sontag, E.D.: Smooth stability implies coprime factorization. IEEE Transaction on Automatic Control 34(4), 435–443 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  12. Sontag, E.D.: Further facts about input to state stabilization. IEEE Transactions on Automatic Control 35(4), 473–476 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  13. Sonag, E.D.: On the input-to-state stability property. European Journal of Control 1(1), 24–36 (1995)

    Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  15. Chu, K.C.: Decentralized control of high speed vehicle string. Transportation Research 8, 361–383 (1974)

    Google Scholar 

  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)

    Article  MATH  Google Scholar 

  17. Swaroop, D., Hedrick, J.K.: String stability of interconnection systems. IEEE Trans.on Automatic Control 41(3), 349–357 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  18. Darbha, S.: A note about the stability of string LTI systems. Journal of Dynamic Systems, Measurement and Control 124(3), 472–475 (2002)

    Article  MathSciNet  Google Scholar 

  19. Hedrick, J.K., Tomizuka, M., Varaiya, P.: Control issues in automated highway systems. IEEE Control System Magazine 14(6), 21–32 (1994)

    Article  Google Scholar 

  20. Pant, A., Seiler, P., Hedrick, K.: Mesh stability of look-ahead interconnected systems. IEEE Transactions on Automatic Control 47(2), 403–407 (2002)

    Article  MathSciNet  Google Scholar 

  21. Marquez, H.J.: Nonlinear Control Systems Analysis and Design. John Wiley & Sons, Hoboken (2003)

    MATH  Google Scholar 

  22. Kokotovic, P., Hhalil, H.K., O’Reilly, J.: Singular Perturbation Methods in Control: Analysis and Design. Academic, New York (1986)

    MATH  Google Scholar 

  23. Hhalil, H.K.: Nonlilear Systems, 3rd edn. Prentice Hall, Upper Sadle River (2002)

    Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

  1. Department of Automation, Nanjing University of Science and Technology, Nanjing, 210094, P.R.C.

    Jia Wang, Xiaobei Wu & Zhiliang Xu

Authors
  1. Jia Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaobei Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhiliang Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computing, Hong Kong Polytechnic University, P.O. Box, Hong Kong, China

    Daniel S. Yeung

  2. School of Creative Media, City University of Hong Kong,, China

    Zhi-Qiang Liu

  3. Department of Mathematics and Computer Science, Hebei University, 071002, Baoding, Hebei, P.R. China

    Xi-Zhao Wang

  4. School of Electrical and Information Engineering, University of Sydney, 2006, NSW, Australia

    Hong Yan

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wang, J., Wu, X., Xu, Z. (2006). Input-to-State Stability Analysis of a Class of Interconnected Nonlinear Systems. In: Yeung, D.S., Liu, ZQ., Wang, XZ., Yan, H. (eds) Advances in Machine Learning and Cybernetics. Lecture Notes in Computer Science(), vol 3930. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11739685_13

Download citation

  • DOI: https://doi.org/10.1007/11739685_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-33584-9

  • Online ISBN: 978-3-540-33585-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics