Robustness to Bounded Inputs and Structured Uncertainty: Analysis and Synthesis

  • Mustafa H. Khammash
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 66)


This paper presents an overview of results on robustness analysis on systems with structured norm bounded uncertainty and bounded inputs (i.e. signals). In addition, the robustness synthesis problem is studied, and new results on globally-optimal controller synthesis for robust performance in the presence of unstructured uncertainty is presented. These results utilize some methods from sensitivity analysis in Linear Programming.


Spectral Radius Robust Stability Robustness Analysis Structure Uncertainty Nominal System 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M. A. Dahleh and M. H. Khammash, Controller Design in the Presence of Uncertainty, Automatica, Vol. 29, No. 1, Jan. 1993, pp. 37–56.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    M. A. Dahleh and Y. Ohta, A necessary and sufficient condition for robust BIRO stability, Systems Sr Control Letters, 11 (1988), pp. 271–275.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    M. A. Dahleh and J. B. Pearson, 1 optimal feedback controllers for mimo discrete time systems, IEEE Transactions on Automatic Control, Vol. AC-32, No. 4, (1987), pp. 314–322.CrossRefGoogle Scholar
  4. [4]
    C. C. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties, Academic Press, New York, 1975.zbMATHGoogle Scholar
  5. [5]
    J. C. Doyle, Analysis of feedback systems with structured uncertainty, IEE Proceedings, Vol. 129, PtD, No. 6, (1982), pp. 242–250.MathSciNetGoogle Scholar
  6. J. C. Doyle, J. E. Wall, and G. Stein, Performance and robustness analysis for structured uncertainty, Proceedings of the 20th IEEE Conference on Decision and Control, (1982), pp. 629–636.Google Scholar
  7. [7]
    R. Horn and C. Johnson, Matrix Analysis, (Cambridge University Press, 1985 ).Google Scholar
  8. M. H. Khammash and J.B. Pearson, Performance robustness of discrete-time systems with structured uncertainty, IEEE Transactions on Automatic Control, Vol. AC-36, (1991), pp. 398–412.MathSciNetCrossRefGoogle Scholar
  9. [9]
    M. H. Khammash, Necessary and Sufficient Conditions for the Robustness of Time-Varying Systems with Applications to Sampled-Data Systems, IEEE Transaction on Automatic Control, Vol. 38, No. 1, Jan. 1993, pp. 49–57.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    M. H. Khammash and J.B. Pearson, Analysis and Design for Robust Performance for Systems with Structured Uncertainty, Systems Sr Control Letters, 20, 1993, pp. 179–187.MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    J.S. McDonald and J.B. Pearson, l 1 optimal control of multivariable systems with output norm constraints, Automatica, vol. 27, No. 2, (1991), pp. 317–329.MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    M. Mendlovitz, A simple solution to the l l optimization problem, Systems & Control Letters, Vol. 12, No. 5, (1989), pp. 461–463.MathSciNetzbMATHCrossRefGoogle Scholar
  13. M.G. Safonov and M. Athans, A multiloop generalization of the circle criterion for stability margin analysis, IEEE Transactions on Automatic Control, vol. AC-26, (1981), pp. 415–422.MathSciNetCrossRefGoogle Scholar
  14. [14]
    M. Safonov, Stability margins of diagonally perturbed multivariable feedback systems, IEE Proceedings, vol. 129, PtD, No. 6, (1982), pp. 251–256.MathSciNetGoogle Scholar
  15. J. Shamma and M. Dahleh, Time-Varying vs. Time-Invariant Compensation for Rejection of Persistent Bounded Disturbances and Robust Stabilization, IEEE Transactions on Automatic Control, Vol. AC-36 (1991), pp. 838–847.MathSciNetCrossRefGoogle Scholar
  16. [16]
    N. Sivashankar and Pramod Khargonekar, Robust Stability Analysis of Sampled-Data Systems, IEEE Transactions on Automatic Control, Vol. 38, No. 1, Jan. 1993, pp. 58–69.MathSciNetzbMATHCrossRefGoogle Scholar
  17. [17]
    O.J. Staffans, Mixed sensitivity minimization problems with rational ti-optimal solutions, Journal of Optimization Theory and Applications, 70 (1991), 173–189.MathSciNetzbMATHCrossRefGoogle Scholar
  18. O.J. Staffans, On the Four-block Model Matching Problem in l 1, Helsinki University of Technology, Espoo, Report A289 (1990).Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

  • Mustafa H. Khammash
    • 1
  1. 1.Electrical Engineering and Computer Engineering DepartmentIowa State UniversityAmesUSA

Personalised recommendations