Abstract
This paper proposes some analytical criteria for controllability and observability analysis of fractional order systems describing by multi-order state space equations. The controllability and observability gramians are presented in which their non-singularity is equivalent to controllability and observability of the mentioned systems. Moreover, to overcome the gramian calculation complexities, the controllability and observability matrices are introduced. It is proved that the sufficient condition for controllability or observability of a multi-order fractional system is that its controllability or observability matrix is nonsingular. Some illustrative examples are given to show the efficiency of the proposed method.
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