Positive linear systems, traditionally investigated within the state-space framework, have been recently analyzed within the behavioral setting, by focusing the attention on the autonomous case. Also, the positive realization problem for autonomous behaviors has been explored in a recent paper. In this contribution, we focus our attention on controllable behaviors.
We first address the general realization problem by means of driving variable state-space representations and later analyze the possibility of realizing a controllable behavior by means of a positive driving variable representation. Several necessary and sufficient conditions for problem solvability are presented.