Doubly coprime representation of linear systems and its application to simultaneous stabilization

This paper develops a new representation theory of multivariabletime-invariant linear systems based on the well-known coprimefactorizations of their transfer matrices. This representationfully uses the algebraic structure of coprime factorizations,and hence has a number of advantages for describing variousproperties of linear systems in simpler and/or more compactforms than the usual transfer matrix representation. In theframework of this new representation theory, various stabilityand stabilizability properties of linear systems are characterizedand finally a simultaneous stabilization problem for a givenset of linear systems is examined.