A convex approach to differential inclusions with prox-regular sets: stability analysis and observer design

Samir Adly, Abderrahim Hantoute, Bat Trang Nguyen

Published 2017-04-17Version 1

We study the existence and stability of solutions for\ differential inclusions governed by the normal cone to a prox-regular set and subject to a Lipschitz perturbation. We prove, that such apparently more general systems can be indeed remodeled into the classical theory of differential inclusions involving maximal monotone operators. This surprising result is new in the literature and permits us to make use of the rich and abundant achievements in this class of monotone operators to derive the desired existence result and stability analysis, as well as the continuity and differentiability properties of the solutions. This going back and forth between these two kinds of differential inclusions is made possible thanks to a viability result for maximal monotone operators. As an application, we study a Luenberger-like observer, which is shown to converge exponentially to the actual state when the initial value of the state's estimation remains in a neighborhood of the initial value of the original system.