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Coprimeness of Fractional Representations

Abstract

Coprimeness of a fractional representation plays various crucial roles in many different contexts, for example, stabilization of a given plant, minimality of a state space representation, etc. It should be noted however that coprimeness depends crucially on the choice of a ring (or algebra) where such a representation is taken, which reflects the choice of a plant, and particular problems that one studies. Such relationships are particularly delicate and interesting when dealing with infinite-dimensional systems. This paper discusses various coprimeness issues for different rings, typically for Hinfinity and pseudorational transfer functions. The former is related to Hinfinity-stabilizability, and the latter to controllability of behaviors. We also give some intricate examples where a seemingly non-coprime factorization indeed turns out to be a coprime factorization over Hinfinity. Some future directions are also indicated.
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Dates and versions

hal-01413310 , version 1 (23-12-2016)

Identifiers

  • HAL Id : hal-01413310 , version 1

Cite

Catherine Bonnet, Yutaka Yamamoto. Coprimeness of Fractional Representations. 55th IEEE Conference on Decision and Control (CDC 2016), Dec 2016, Las Vegas, United States. ⟨hal-01413310⟩
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