Journal of Convex Analysis 32 (2025), No. 3, 681--722
Copyright Heldermann Verlag 2025
Well-Posedness of Passive Time-Varying Linear Cone Complementarity Systems
Quang Hung Pham
Université Grenoble Alpes, INRIA, CNRS, Grenoble INP, LJK, Grenoble, France
quang-hung.pham@inria.fr
Bernard Brogliato
Université Grenoble Alpes, INRIA, CNRS, Grenoble INP, LJK, Grenoble, France
bernard.brogliato@inria.fr
Félix A. Miranda-Villatoro
Université Grenoble Alpes, INRIA, CNRS, Grenoble INP, LJK, Grenoble, France
felix.miranda-villatoro@inria.fr
This article provides sufficient conditions to ensure the existence and uniqueness of absolutely continuous and bounded variation solutions of a family of time-dependent nonsmooth systems named time-varying linear cone complementarity systems. Passivity is a key property. Nonsmooth circuits illustrate the theoretical results.
Keywords: Linear complementarity system, time-varying linear cone complementarity system, first-order sweeping process, well-posedness, linear complementarity problem, set-valued mapping, maximal monotone operator, time-dependent differential inclusion, passive system.
MSC: 34K09, 90C33.
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