Journal of Convex Analysis 29 (2022), No. 2, 481--517
Copyright Heldermann Verlag 2022
Analysis of the Implicit Euler Time-Discretization of a Class of Descriptor-Variable Linear Cone Complementarity Systems
Bernard Brogliato
Université Grenoble Alpes, INRIA, CNRS, Grenoble, France
bernard.brogliato@inria.fr
This article is largely concerned with the time-discretization of a class of descriptor-variable systems coupled with complementarity constraints, named descriptor-variable linear complementarity systems (DVLCS). Specifically, the Euler implicit discretization of DVLCS is analysed: the one-step non-smooth problem, which is a generalized equation, is shown to be well-posed under some conditions. Then the convergence of the discretized solutions is studied, and the existence of solutions to the continuous-time system is shown as a consequence. Several circuits examples illustrate the applicability and the theoretical developments.
Keywords: Differential-algebraic system, descriptor-variable system, linear complementarity system, sweeping process, recession function, Euler discretisation, well-posedness, passive system.
MSC: 65K15, 94C60, 49J53, 34A09, 34A12, 34A60.
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