2017/04/17 by Samir Adly, Adly, Samir, Abderrahim Hantoute +3
Computer Science · Engineering · Mathematics · #Optimization and Variational Analysis #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations #math.OC
paper · pdf · doi:10.48550/arxiv.1704.04913
32 pages
arxiv created 2018/01/22 · arxiv updated 2018/01/23
In this paper, we study the existence and the stability in the sense of Lyapunov of solutions for differential inclusions governed by the normal cone to a prox-regular set and subject to a Lipschitzian perturbation. We prove that such, apparently, more general nonsmooth dynamics can be indeed remodelled into the classical theory of differential inclusions involving maximal monotone operators. This 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 models 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.