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

Bernard Brogliato ⁽¹⁾, Alexandre Rocca ⁽¹⁾

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

Bernard Brogliato ⁽¹⁾, Alexandre Rocca ⁽¹⁾

(1) Modélisation, simulation et commande des systèmes dynamiques non lisses

Abstract

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.

Keywords

• [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
• [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
• descriptor-variable systems
• linear complementarity systems
• implicit Euler scheme
• convergence
• electrical circuits

Mathematics Subject Classification 2020

• 93C05 - Linear systems in control theory
• 93C15 - Control/observation systems governed by ordinary differential equations
• 93C55 - Discrete-time control/observation systems

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