Equivalence transformations in linear dynamical systems†

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Abstract
The authors analyse the equivalonce of the minimal realizations of linear dynamical systems with given properties. To this end thoy review various groups of equivalence transformations, somo of which are already known while others are introduced for the first time in this paper. More particularly, the authors study the equivalence of the minimal and periodic realizations, as well as that of the minimal, bounded and reduced realizations. For these latter they also state tho necessary and sufficient conditions governing their existence.