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Abstract
We give many necessary and sufficient conditions for the existence of a weakly coprime or Bezout coprime factorization of a transfer function, possibly operator valued. Some of these conditions are given in terms of the output- or state-feedback stabilizability of realizations. Our realizations are well-posed linear systems—continuous-time linear time-invariant infinite-dimensional systems. We also study further properties of such factorizations, their relations to discrete-time weakly coprime factorizations, counterexamples and (weak) left invertibility. Moreover, analogous discrete-time results are obtained. Control-theoretic consequences are indicated.
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