On Realization Theory for Generalized State-Space Systems over a Commutative Ring

  • J. Daniel Cobb
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 62)


The problem of finding a state-space realization for a given rational matrix over a commutative ring is considered. To simplify the problem, we assume a certain factored structure for the denominator polynomials in the matrix. Our main results state that this class of matrices is a module which can be decomposed into two independent and isomorphic submodules, each realizable via existing results for strictly proper matrices. Any rational matrix with factored denominators can be realized through this decomposition.

Key words

algebraic systems realization theory singular systems singular perturbation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    F.L. Lewis, A survey of linear singular systems, Circuits, Systems, and Signal Processing, Vol. 5, No. 1, 1986.Google Scholar
  2. [2]
    M.F. Atiyah, I. G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley, 1969.zbMATHGoogle Scholar
  3. [3]
    J.W. Brewer, J.W. Bunce, F.S. Van Vleck, Linear Systems over Commutative Rings, Marcel Dekker, New York, 1986.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1994

Authors and Affiliations

  • J. Daniel Cobb
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of Wisconsin-MadisonMadisonUSA

Personalised recommendations