Abstract
Abstract This short discussion note is devoted to establishing some connections between the framework of dynamical systems driven by signals of a low regularity (rough differential equations) and the mathematical theory of impulsive control (measure-driven systems), which, as we believe, would essentially enrich one another. More precisely, we attempt to elaborate an impulsive (discontinuous) extension of the theory of rough differential equation for input-affine models with states of unbounded first variation. In the paper, we are focused on a concept of solution for impulsive rough differential equations with vector-valued controls of bounded p-variation, p£ (1,2), and its constructive representation through a (discrete-continuous) Young’s integral equation.
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