Computation and Control pp 277-282 | Cite as

# Tuning Natural Frequencies by Output Feedback

Chapter

## Abstract

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.

## Preview

Unable to display preview. Download preview PDF.

## References

- [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.MathSciNetMATHCrossRefGoogle Scholar - [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]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.MathSciNetMATHCrossRefGoogle Scholar - [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.MathSciNetMATHCrossRefGoogle Scholar - [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]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.MathSciNetMATHCrossRefGoogle Scholar - [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.MathSciNetMATHCrossRefGoogle Scholar - [8]H. Kimura, “Pole Assignment by Gain Output Feedback,”
*IEEE Trans. Aut. Contr*., v. 20, 1975, pp. 509–516.MATHCrossRefGoogle Scholar - [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.MATHCrossRefGoogle Scholar - [10]S. L. Kleinman and D. Laksov, “Schubert Calculus,”
*Amer. Math. Monthly, v*. 79, 1975, pp. 1061–1082.CrossRefGoogle Scholar - [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.MathSciNetMATHCrossRefGoogle Scholar - [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