Linear Algebra for Control Theory pp 55-60 | Cite as

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

Conference paper

## Abstract

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## Preview

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## References

- [1]F.L. Lewis,
*A survey of linear singular systems*, Circuits, Systems, and Signal Processing, Vol. 5, No. 1, 1986.Google Scholar - [2]M.F. Atiyah, I. G. MacDonald,
*Introduction to Commutative Algebra*, Addison-Wesley, 1969.zbMATHGoogle Scholar - [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