Nonnegative realization of autonomous systems in the behavioral approach

Nonnegative linear systems, which hav traditionally been investigated withi n the state-space framework, hav been recently introduced and analyzed by m eans of the behavioral approach. In a couple of recent papers [J. W. Nieuwe nhuis, Linear Algebra Appl., 281 (1998), pp. 43-58, M. E. Valcher, Linear A lgebra Appl., 319 (2000), pp. 147-162], several general definitions and res ults about nonnegative behaviors, as well as a complete analysis of nonnega tivity property for autonomous behaviors, hav been presented. In this contr ibution, by focusing our interest again on autonomous behaviors, we explore the nonnegative realization problem by deriving an extended set of necessa ry and sufficient ( geometric) conditions for an autonomous behavior to be nonnegative realizable. In the scalar case, in particular, necessary and su fficient conditions for nonnegative realizability, which refer to the set o f zeros of any polynomial involved in the kernel description of the behavio r, are provided. Finally, a comparison between the nonnegative realizabilit y 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.