ANALYSIS OF THE IMPLICIT EULER TIME-DISCRETIZATION OF SEMIEXPLICIT DIFFERENTIAL-ALGEBRAIC LINEAR COMPLEMENTARITY SYSTEMS\ast

This article is largely concerned with the time-discretization of differential-algebraic equations (DAEs) with complementarity constraints, which we name differential-algebraic linear complementarity systems (DALCSs). Specifically, the Euler implicit discretization of DALCSs is analyzed: the one-step nonsmooth 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. Passivity of some operators is pivotal to the analysis. Examples from circuits, mechanics, and switching DAEs illustrate the applicability of the developments.