Nagumo's Theorem for Dubovitskij-Miljutin Tangent Cones

Abstract

This paper focuses on a class of additive perturbations in dynamical systems. An equivalence statement for this construction is discovered, and consequently, a method of checking a notion of positive invariance with perturbation. The resulting conclusion is an equivalence between a more strict definition of positive invariance, based on a perturbation extension of the system and the Dubovitskij-Miljutin tangent cone.