Abstract
Notions of the externally and internally positive standard and singular discrete-time and continuous-time linear systems are introduced. Necessary and sufficient conditions for the external and internal positivity of linear systems are given. It is shown that the reachability and controllability of the internally positive linear systems are not invariant under the state-feedbacks. By suitable choice of the state-feedbacks an unreachable internally positive linear systems can be made reachable and a controllable internally positive system can be made uncontrollable. The basic properties of continuous-time and discrete-time linear compartmental systems are derived and the relationships between the compartmental and positive systems are established. The realization problem for compartmental systems is formulated and partly solved.
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