Skip to main content

Structured dissipativity and absolute stability of nonlinear systems

  • Conference paper
  • First Online:
Robust Control via Variable Structure and Lyapunov Techniques

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 217))

  • 254 Accesses

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Byrnes, C. I., Isidori, A., Willems, J. C., 1991, Passivity, feedback equivalence, and global stabilization of minimum phase nonlinear systems, IEEE Transactions on Automatic Control, 36(11), 1228–1240.

    Google Scholar 

  • Doyle, J. C., 1982, Analysis of feedback systems with structured uncertainty, IEEE Proceedings Part D, 129(6), 242–250.

    Google Scholar 

  • Hill, D., Moylan, P., 1976, The stability of nonlinear dissipative systems, IEEE Transactions on Automatic Control, 21, 708–711.

    Google Scholar 

  • Hill, D., Moylan, P., 1977, Stability results for nonlinear feedback systems, Automatica, 13, 377–382.

    Google Scholar 

  • Hill, D., Moylan, P., 1980, Dissipative dynamical systems: Basic input-output and state properties, Journal of the Franklin Institute, 309, 327–357.

    Google Scholar 

  • Khammash, M., Pearson, J. B., 1993, Analysis and design for robust performance with structured uncertainty, Systems and Control Letters, 20(3), 179–188.

    Google Scholar 

  • Megretsky, A., 1993, Necessary and sufficient conditions of stability: A multiloop generalization of the circle criterion, IEEE Transactions on Automatic Control, 38(5), 753–756.

    Google Scholar 

  • Megretsky, A., Treil, S., 1993, Power distribution inequalities in optimization and robustness of uncertain systems, Journal of Mathematical Systems, Estimation and Control, 3(3), 301–319.

    Google Scholar 

  • Rockafellar, R. T., 1970, Convex Analysis, Princeton University Press, Princeton, NJ.

    Google Scholar 

  • Safonov, M. G., 1982, Stability margins of diagonally perturbed multivariable feedback systems, IEE Proceedings Part D, 129(6), 251–256.

    Google Scholar 

  • Savkin, A. V., Petersen, I. R., 1994, A connection between H ∞ control and the absolute stabilizability of uncertain systems, Systems and Control Letters, 23(3), 197–203.

    Google Scholar 

  • Savkin, A. V., Petersen, I. R., 1995a, Minimax optimal control of uncertain systems with structured uncertainty, International Journal of Robust and Nonlinear Control, 5(2), 119–137.

    Google Scholar 

  • Savkin, A. V., Petersen, I. R., 1995b, Nonlinear versus linear control in the absolute stabilizability of uncertain linear systems with structured uncertainty, IEEE Transactions on Automatic Control, 40(1), 122–127.

    Google Scholar 

  • Shamma, J. S., 1992, Robustness analysis for time-varying systems, Proceedings IEEE Conference on Decision and Control, Tucson, Arizona.

    Google Scholar 

  • Uhlig, F., 1979, A recurring theorem about pairs of quadratic forms and extensions: A survey, Linear Algebra and its Applications, 25, 219–237.

    Google Scholar 

  • Willems, J. C., 1972, Dissipative dynamical systems—part I: General theory, Archive of Rational Mechanics and Analysis, 45, 321–351.

    Google Scholar 

  • Yakubovich, V. A., 1971, S-procedure in nonlinear control theory, Vestnik Leningrad University, Series 1, 13(1), 62–77.

    Google Scholar 

  • Yakubovich, V. A., 1973, Minimization of quadratic functionals under the quadratic constraints and the necessity of a frequency condition in the quadratic criterion for absolute stability of nonlinear control systems, Soviet Mathematics Doklady, 14, 593–597.

    Google Scholar 

  • Yakubovich, V. A., 1988a, Absolute stability of nonlinear systems with a periodically nonstationary linear part, Soviet Physics Doklady, 32(1), 5–7.

    Google Scholar 

  • Yakubovich, V. A., 1988b, Dichotomy and absolute stability of nonlinear systems with periodically nonstationary linear part, Systems and Control Letters, 11(3), 221–228.

    Google Scholar 

Download references

Authors

Editor information

Franco Garofalo Luigi Glielmo

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag London Limited

About this paper

Cite this paper

Savkin, A.V., Petersen, I.R. (1996). Structured dissipativity and absolute stability of nonlinear systems. In: Garofalo, F., Glielmo, L. (eds) Robust Control via Variable Structure and Lyapunov Techniques. Lecture Notes in Control and Information Sciences, vol 217. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027571

Download citation

  • DOI: https://doi.org/10.1007/BFb0027571

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-76067-2

  • Online ISBN: 978-3-540-40946-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics