Nonnegative realization of autonomous systems in the behavioral approach

Nonnegative linear systems, which have traditionally been investigated within the state-space framework, have been recently introduced and analyzed by means of the behavioral approach. In a couple ofrecen t papers [J. W. Nieuwenhuis, Linear Algebra Appl., 281 (1998), pp. 43–58, M. E. Valcher, Linear Algebra Appl., 319 (2000), pp. 147–162], several general definitions and results about nonnegative behaviors, as well as a complete analysis ofnonnegativit y property for autonomous behaviors, have been presented. In this contribution, by focusing our interest again on autonomous behaviors, we explore the nonnegative realization problem by deriving an extended set ofnecessary and sufficient (geometric) conditions for an autonomous behavior to be nonnegative realizable. In the scalar case, in particular, necessary and sufficient conditions for nonnegative realizability, which refer to the set ofzeros ofan y polynomial involved in the kernel description of the behavior, are provided. Finally, a comparison between the nonnegative realizability property, here investigated, and K-realizability, addressed in [H. Maeda and S. Kodama, IEEE Trans. Circuits, Systems I Fund. Theory Appl., CAS-281 (1981), pp. 39–47] is carried on.