Skip to main content
SpringerLink
Log in

Decentralized robust control for a class of uncertain large-scale interconnected nonlinear dynamical systems

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

The problem of the decentralized robust control for a class of large-scale interconnected nonlinear dynamical systems with input interconnection and external interconnection perturbations is considered. Based on the stabilizability of each nominal isolated subsystem (i.e., the isolated subsystem in the absence of interconnection perturbations), a class of decentralized local state feedback controllers is proposed, and some sufficient conditions are derived by making use of the Lyapunov stability criterion such that uncertain large-scale interconnected systems can be stabilized asymptotically by these decentralized state feedback controllers. For large-scale systems with only input interconnection perturbations, such decentralized controllers become a class of decentralized stabilizing state feedback controllers. That is, the decentralized stability of such large-scale systems can be guaranteed always by using the decentralized state feedback controllers proposed in the paper. Finally, a numerical example is given to demonstrate the validity of the results.

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. Ailjak, D. D.,Large-Scale Dynamic Systems: Stability and Structure, North Holland, Amsterdam, Holland, 1978.

    Google Scholar 

  2. Mahmoud, M. S., Hassan, M. F., andDarwish, M. G.,Large-Scale Control Systems: Theories and Techniques, Marcel Dekker, New York, New York, 1985.

    Google Scholar 

  3. Siljak, D. D.,Decentralized Control of Complex Systems, Academic Press, New York, New York, 1991.

    Google Scholar 

  4. Davison, E. J.,The Decentralized Stabilization and Control of a Class of Unknown Nonlinear Time-Varying Systems, Automatica, Vol. 10, pp. 309–316, 1974.

    Google Scholar 

  5. Sezer, M. E., andHuseyin, O.,Stabilization of Linear Time-Invariant Interconnected Systems Using Local State Feedback, IEEE Transactions on Systems, Man, and Cybernetics, Vol. 8, pp. 751–756, 1978.

    Google Scholar 

  6. Siljak, D. D., andVukcevic, M. B.,Decentrally Stabilizable Linear and Bilinear Large-Scale Systems, International Journal of Control, Vol. 26, pp. 289–305, 1977.

    Google Scholar 

  7. Wang, S. H.,An Example in Decentralized Control Systems, IEEE Transactions on Automatic Control, Vol. 23, pp. 938–939, 1978.

    Google Scholar 

  8. Ikeda, M., Umefuji, O. andKodama, S.,Stabilization of Large-Scale Linear Systems, Transactions of the Institute of Electronics, Information, and Communication Engineers of Japan, Vol. 59D, pp. 355–362, 1976.

    Google Scholar 

  9. Ikeda, M., andSiljak, D. D.,Decentralized Stabilization of Linear Time-Varying Systems, IEEE Transactions onAutomatic Control, Vol. 25, pp. 106–107, 1980.

    Google Scholar 

  10. Shi, Z. C., andGao, W. B.,Decentralized Stabilization of Time-Varying Largescale Interconnected Systems, International Journal of Systems Science, Vol. 18, pp. 1523–1535, 1987.

    Google Scholar 

  11. Chen Y. H.,Decentralized Robust Control System Design for Large-Scale Uncertain Systems, International Journal of Control, Vol. 47, pp. 1195–1205, 1988.

    Google Scholar 

  12. Wang, W. J., Cheng, C. F., andLee, T. T.,Stabilization of Large-Scale Systems with Nonlinear Perturbations via Local Feedback, International Journal of Systems Science, Vol. 20, pp. 1003–1010, 1989.

    Google Scholar 

  13. Wu, H.,Decentralized Robust Control for a Class of Large-Scale Interconnected Systems with Uncertainties, International Journal of Systems Science, Vol. 20, pp. 2597–2608, 1989.

    Google Scholar 

  14. Ho, S. J., Horng, I. R., andChou, J. H.,Decentralized Stabilization of Large-Scale Systems with Structured Uncertainties, International Journal of Systems Science, Vol. 23, pp. 425–434, 1992.

    Google Scholar 

  15. Franklin, J. N.,Matrix Theory, Prentice-Hall, Englewood Cliffs, New Jersey, 1968.

    Google Scholar 

  16. Desoer, C. A., andVidyasagar M.,Feedback System: Input-Output Properties, Academic Press, New York, New York, 1975.

    Google Scholar 

  17. Chen, Y. H., Leitmann, G., andKai, X. Z.,Robust Control Design for Interconnected Systems with Time-Varying Uncertainties, International Journal of Control, Vol. 54, pp. 1119–1142, 1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Engineering, Hiroshima University, Kagamiyama, Higashi-Hiroshima City, Japan

    S. Y. Zhang (Graduate Student)

  2. Division of Mathematical and Information Sciences, Faculty of Integrated Arts and Sciences, Hiroshima University, Kagamiyama, Higashi-Hiroshima City, Japan

    K. Mizukami (Professor) & H. S. Wu (Associate Professor)

Authors
  1. S. Y. Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Mizukami
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. S. Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by G. Leitmann

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, S.Y., Mizukami, K. & Wu, H.S. Decentralized robust control for a class of uncertain large-scale interconnected nonlinear dynamical systems. J Optim Theory Appl 91, 235–256 (1996). https://doi.org/10.1007/BF02192291

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02192291

Key Words

Search

Navigation