Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Keywords

  • Differential-algebraic system
  • descriptor-variable system
  • linear complementarity system
  • sweeping process
  • recession function
  • Euler discretisation
  • well-posedness
  • passive system

Mathematics Subject Classification

65K15, 94C60, 49J53, 34A09, 34A12, 34A60

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Suggested citation

B. Brogliato. “Analysis of the Implicit Euler Time-Discretization of a Class of Descriptor-Variable Linear Cone Complementarity Systems.” Journal of Convex Analysis 29 (2022), No. 2, 481–517. https://doi.org/10.68381/jca29029

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