Tuning Natural Frequencies by Output Feedback

  • J. Rosenthal
Part of the Progress in Systems and Control Theory book series (PSCT, volume 1)


The following paper considers the problem of static output feedback for a linear, time invariant system. Starting from a geometric model a new algorithm for finding a linear feedback law is derived. The well known condition m + p - 1 ≥ n for generic pole placement given by Kimura [8] is improved using geometric arguments in linear spaces.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. W. Brockett and C. I. Byrnes, “Multivariable Nyquist Criteria, Root Loci, and Pole Placement: A Geometric Viewpoint,” IEEE Trans. Aut. Contr., AC-26, 1981, pp. 271–284.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    C. I. Byrnes, “Algebraic and Geometric Aspects of the Analysis of Feedback Systems,” in Geometric Methods in Control Theory, C. I. Byrnes and C. F. Martin, eds., Reidel, Dodrecht, Holland, 1980. pp. 85–124.Google Scholar
  3. [3]
    C. I. Byrnes, “Stabilizability of Multivariable Systems and the Ljusternik- Snirelmann Category of Real Grassmannians,” System and Control Letters, v. 3, 1983, pp. 255–262.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    C. I. Byrnes and B. D. 0. Anderson, “Output Feedback and Generic Stabilizability,” SIAM J. Control, v. 22, no. 3, 1984, pp. 362–380.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    C. I. Byrnes and P. K. Stevens, “Global Properties of the Root Locus Map,” in Feedback Control of Linear and Nonlinear Systems, Lecture Notes in Control and Inf. Sciences, v. 39, Springer Verlag, Berlin, 1982.Google Scholar
  6. [6]
    B. K. Ghosh, “An Approach to Simultaneous System Design, Part II: Nonswitching Gain and Dynamic Feedback Compensation by Algebraic Geometric Methods,” SIAM J. Control, v. 26, no. 4, 1988, pp. 919–963.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    R. Hermann and C. F. Martin, “Applications of Algebraic Geometry to System Theory-Part I,” IEEE Trans. Ant. Contr., v. 22, 1977, pp. 19–25.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    H. Kimura, “Pole Assignment by Gain Output Feedback,” IEEE Trans. Aut. Contr., v. 20, 1975, pp. 509–516.zbMATHCrossRefGoogle Scholar
  9. [9]
    H. Kimura, “A Further Result in the Problem of Pole Assignment by Output Feedback,” IEEE Trans. Aut. Contr., v. 22, 1977, pp. 458–463.zbMATHCrossRefGoogle Scholar
  10. [10]
    S. L. Kleinman and D. Laksov, “Schubert Calculus,” Amer. Math. Monthly, v. 79, 1975, pp. 1061–1082.CrossRefGoogle Scholar
  11. [11]
    C. F. Martin and R. Hermann, “Applications of Algebraic Geometry to System Theory: The McMillan Degree and Kronecher Indices as Topological and Holomorphic Invariants,” SIAM J. Control, v. 16, no. 5, 1978, pp. 743–755.MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    J. C. Willems and W. H. Hesselink, “Generic Properties of the Pole-Placement Problem,” in Proc. of the 1978 IFAC, Helsinki, Finland.Google Scholar

Copyright information

© Birkhäuser Boston 1989

Authors and Affiliations

  • J. Rosenthal
    • 1
  1. 1.Department of MathematicsArizona State UniversityTempeUSA

Personalised recommendations