Abstract
The reachability and controllability to zero of standard and positive fractional linear discrete-time systems are addressed. Necessary and sufficient conditions for the controllability of standard fractional discrete-time systems are established. New tests for checking the reachability and controllability to zero of the standard fractional systems are presented. A notion of positive fractional linear discrete-time systems is introduced. Necessary and sufficient conditions for the positivity, reachability and controllability to zero of fractional discrete-time systems are given.
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