Analysis of the implicit Euler time-discretization of passive linear descriptor complementarity systems

Bernard Brogliato (1) , Alexandre Rocca (1)

1 TRIPOP - Modélisation, simulation et commande des systèmes dynamiques non lisses

This article is largely concerned with the time-discretization of descriptor-variable systems coupled to with complementarity constraints. They are named descriptor-variable linear complementarity systems (DVLCS). More speci cally passive DVLCS with minimal state space representation are studied. The Euler implicit discretization of DVLCS is analysed: the one-step non-smooth problem (OSNSP), that is a generalized equation, is shown to be well-posed under some conditions. Then the convergence of the discretized solutions is studied. Several examples illustrate the applicability and the limitations of the developments.

Mots clés: descriptor-variable systems; linear complementarity systems; implicit Euler scheme; convergence; electrical circuits

Domaines: Analyse numérique [math.NA]; Optimisation et contrôle [math.OC]

Bernard Brogliato, Alexandre Rocca. Analysis of the implicit Euler time-discretization of passive linear descriptor complementarity systems. Journal of Nonsmooth Analysis and Optimization, 2022, Volume 3, paper 7269. ⟨10.46298/jnsao-2022-7269⟩. ⟨hal-03169123v3⟩