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## Section: New Results

### Stabilization of MIMO fractional systems with delays

Participants : Catherine Bonnet, Le Ha Vy Nguyen, Alban Quadrat.

In order to yield the set of all stabilizing controllers of a large class of MIMO fractional time-delay systems, we may look for coprime factorizations of the transfer function and their corresponding Bézout factors. As primary results, in considering ${H}_{\infty }$ stability, left coprime factorizations and left Bézout factors have been determined analytically from the transfer function. Then a particular stabilizing controller has been derived. We also proved the existence of right coprime factorizations.