The positive and cone fractional continuous-time and discrete-time linear systems are addressed. Sufficient conditions for the reachability of positive and cone fractional continuous-time linear systems are given. Necessary and sufficient conditions for the positivity and asymptotic stability of the continuous-time linear systems with delays are established. The realization problem for positive fractional continuous-time systems is formulated and solved. Necessary and sufficient conditions for the positivity and practical stability of fractional linear discrete-time systems are established. The linear matrix inequality (LMI) approaches are applied to testing the asymptotic stability of the positive fractional discrete-time linear systems. Sufficient conditions for the existence are established and procedures for computation of positive and cone realizations of the discrete-time linear systems are proposed.

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