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IMA Journal of Mathematical Control and Information 2003 20(1):21-35; doi:10.1093/imamci/20.1.21
© 2003 by Institute of Mathematics and its Applications
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Doubly coprime representation of linear systems and its application to simultaneous stabilization

Hiroshi Inaba1, Rixat Abdursul1 and Satoru Takahashi1

1 Department of Information Sciences, Tokyo Denki University, Hatoyama-Machi, Hiki-Gun, Saitama 350-0394, Japan

This paper develops a new representation theory of multivariable time-invariant linear systems based on the well-known coprime factorizations of their transfer matrices. This representation fully uses the algebraic structure of coprime factorizations, and hence has a number of advantages for describing various properties of linear systems in simpler and/or more compact forms than the usual transfer matrix representation. In the framework of this new representation theory, various stability and stabilizability properties of linear systems are characterized and finally a simultaneous stabilization problem for a given set of linear systems is examined.

Keywords: transfer matrix; doubly coprime factorization; simultaneous stabilizability.

Received 14 February 2002. Accepted 1 May 2002.


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