A note on discrete-time positive realizations

A discrete-time positive linear system has the property that any nonnegative initial state and any nonnegative input produces a nonnegative trajectory in the state space and output for all time. Such systems are Rn+-reachable if every state of the nonnegative orthant Rn+ is reachable from origin with a nonnegative input function, in a finite-time interval. A simple necessary and sufficient condition for Rn+-realizability, i.e. for the existence of a nonnegative realization that is also Rn+-reachable, is stated. The realization procedure is straightforward.