A NOTE ON THE CONTROLLABILITY AND THE OBSERVABILITY OF FRACTIONAL DYNAMICAL SYSTEMS

In this paper, we give some new results on the controllability and the observability of linear dynamical systems with a fractional derivative of order α, where α is a non integer number. We show that the observability and the controllability Gramians, recently introduced for a fractional order system, are solutions of fractional differential Lyapunov equations, thus generalizing the classical result for the integer case (α = 1). Our results can be considered as a generalization of the known corresponding results in the integer order case to the fractional order one since for α = 1, the results for the integer case are recovered.