The paper introduces and studies differentially positive systems, that is,
systems whose linearization along an arbitrary trajectory is positive. A
generalization of Perron Frobenius theory is developed in this differential
framework to show that the property induces a (conal) order that strongly
constrains the asymptotic behavior of solutions. The results illustrate that
behaviors constrained by local order properties extend beyond the well-studied
class of linear positive systems and monotone systems, which both require a
constant cone field and a linear state space.The research was supported by the Fund for Scientific Research FNRS and by the Engineering and Physical Sciences Research Council under Grant EP/G066477/1.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/TAC.2015.243752
