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New Results on the Controllability and Observability of Fractional Dynamical Systems

In this article, we describe some new results on the controllability and observability of linear dynamical systems involving a fractional derivative of order α. We show that the input control energy required to drive the state in a given direction and the energy available at the output are related to the observability and the controllability Gramians, respectively. Our results can be considered as a generalization of the known corresponding results for the integer order case to the fractional order one, since for α 1 1, the results for the integer case are recovered.