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System zeros and the weakly unobservable subspace

  • Harry L. Trentelman
  • Anton A. Stoorvogel
  • Malo Hautus
Part of the Communications and Control Engineering book series (CCE)

Abstract

In this chapter we first give a brief review of some elementary material on polynomial matrices and the Smith form. We then continue our study of the system ∑ given by the equations

1(t) = Ax(t) + Bu(t), y(t) = Cx(t) + Du(t)

and introduce an important polynomial matrix associated with this system, the system matrix of ∑. Using the system matrix, we introduce the concepts of transmission polynomials, and zeros of the system ∑. Next, we discuss the weakly unobservable subspace, and the controllable weakly unobservable subspace associated with ∑. The weakly unobservable subspace is used to give a geometric characterization of the property of strong observability. We conclude this chapter with a characterization of the transmission polynomials and the zeros of ∑ in terms of the weakly unobservable and controllable weakly unobservable subspace.

Keywords

Subspace Versus Polynomial Matrix Invariant Factor Full Column Rank Polynomial Matrice 
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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Copyright information

© Springer-Verlag London 2001

Authors and Affiliations

  • Harry L. Trentelman
    • 1
  • Anton A. Stoorvogel
    • 2
  • Malo Hautus
    • 2
  1. 1.Department of MathematicsUniversity of GroningenGroningenThe Netherlands
  2. 2.Department of Mathematics and Computing ScienceEindhoven University of TechnologyEindhovenThe Netherlands

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