Feedback Systems Stabilizability in Terms of Invariant Zeros

  • Giovanni Marro
  • Aurelio Piazzi
Chapter
Part of the Progress in Systems and Control Theory book series (PSCT, volume 12)

Abstract

It is well known that zeros play a very basic role in the analysis and synthesis of multivariable systems: although the term “zero” clearly comes from the polynomial (transfer matrix) approach, in the early 70’s it was extended to the state-space description through geometric tools and techniques [1, 2]. In particular, the invariant zeros of a triple (A, B, C) are defined both as the roots with multiplicity of the invariant polynomials of the Rosenbrock system matrix [3] and as the internal unassignable eigenvalues with multiplicity of the maximal (A, imB)-controlled invariant contained in kerC [4, 5].

Keywords

State Feedback Feedback System Regulator Problem Disturbance Localization Multivariable 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.

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References

  1. [1]
    A.S. Morse, Structural invariants of linear multivariable systems, in SIAM J. Control, 11 (1973), 446–465.Google Scholar
  2. [2]
    B.P. Molinari, Zeros of the system matrix,in IEEE Trans. Autom. Contr., AC-21(1976), 795–797.Google Scholar
  3. [3]
    H.H.Rosenbrock, State space and multivariable theory, Wiley, New York, 1970.Google Scholar
  4. [4]
    A.G.J. Macfarlane and K. Karcanias, Poles and zeros of linear multivariable systems: a survey of the algebraic, geometric, and complex-variable theory, in International J. Control, 24 (1976), 33–74.CrossRefGoogle Scholar
  5. [5]
    C.B. Schrader and M.K. Sain, Research on system zeros: a survey in International J. Control, 50 (1989), 1407–1433.CrossRefGoogle Scholar
  6. [6]
    G. Basile and G. Marro, Self-bounded controlled invariants: a straightforward approach to constrained controllability, in J. Optimiz. Th. Applic., 38 (1982), 71–81.CrossRefGoogle Scholar
  7. [7]
    J.M. Schumacher, On a conjecture of Basile and Marro, in J. Optimiz. Th. Applic., 41 (1983), 371–376.CrossRefGoogle Scholar
  8. [8]
    G. Basile and G. Marro, Self-bounded controlled invariants versus stabilizability, in J. Optimiz. Th. Applic., 48 (1986), 245–263.CrossRefGoogle Scholar
  9. [9]
    G. Basile and G. Marro, Controlled and conditioned invariants in linear system theory, Prentice Hall, Englewood Cliffs, 1991.Google Scholar
  10. [10]
    G. Basile, G. Marro and A. Piazzi, A new solution to the disturbance localization problem with stability and its dual,in Proceedings of the ‘84 International AMSE Conference on Modelling and Simulation, 12(1984), 19–27, Athens.Google Scholar
  11. [11]
    G. Basile, G. Marro and A. Piazzi, Stability without eigenspaces in the geometric approach: some new results, in Frequency domain and state space methods for linear systems, C.A. Byrnes and A. Lindquist, 1986, North-Holland, 441–450.Google Scholar
  12. [12]
    G. Basile, G. Marro and A. Piazzi, Stability without eigenspaces in the geometric approach: the regulator problem, in in J. Optimiz. Th. Applic., 64 (1990), 29–42.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Giovanni Marro
    • 1
  • Aurelio Piazzi
    • 1
  1. 1.D.E.I.S.Università di BolognaBolognaItaly

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