Abstract
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.
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