
Journal of Convex Analysis 29 (2022), No. 2, 481517 Copyright Heldermann Verlag 2022 Analysis of the Implicit Euler TimeDiscretization of a Class of DescriptorVariable Linear Cone Complementarity Systems Bernard Brogliato Université Grenoble Alpes, INRIA, CNRS, Grenoble, France bernard.brogliato@inria.fr This article is largely concerned with the timediscretization of a class of descriptorvariable systems coupled with complementarity constraints, named descriptorvariable linear complementarity systems (DVLCS). Specifically, the Euler implicit discretization of DVLCS is analysed: the onestep nonsmooth problem, which is a generalized equation, is shown to be wellposed under some conditions. Then the convergence of the discretized solutions is studied, and the existence of solutions to the continuoustime system is shown as a consequence. Several circuits examples illustrate the applicability and the theoretical developments. Keywords: Differentialalgebraic system, descriptorvariable system, linear complementarity system, sweeping process, recession function, Euler discretisation, wellposedness, passive system. MSC: 65K15, 94C60, 49J53, 34A09, 34A12, 34A60. [ Fulltextpdf (271 KB)] for subscribers only. 