Nonnegative linear systems in the behavioral approach: the autonomous case

Nonnegative linear systems, which have traditionally been investigated within the statespace framework, are in this paper introduced and analyzed by means of the behavioral approach. Starting from certain definitions and results presented in a recent paper [J.W. Nieuwenhuis, Systems Control Lett. 1 (1982) 283], we have explored the general autonomous case, by deriving an extended set of necessary and sufficient conditions for an autonomous behavior to be nonnegative. In the scalar case, in particular, necessary conditions for nonnegativity, which refer to the set of zeros of any polynomial involved in the kernel description of the behavior, have been provided.