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Existence and Uniqueness of Solutions for Non-Autonomous Complementarity Dynamical Systems

Bernard Brogliato 1 Lionel Thibault 2
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK [2007-2015] - Laboratoire Jean Kuntzmann [2007-2015], Grenoble INP [2007-2019] - Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019]
Abstract : This paper deals with the well-posedness of a class of complementarity dynamical systems. Both the linear and the nonlinear cases are treated, and the systems are non-autonomous. A specific "inputoutput" property is used to perform a change of state vector which allows one to transform the complementarity dynamics into a perturbed Moreau's sweeping process. Then the results obtained elsewhere by Thibault and his co-workers [16, 15, 40] on the well-posedness of the sweeping process are used. Absolutely continuous as well as bounded variation solutions (with state jumps) are examined in this work.
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Bernard Brogliato, Lionel Thibault. Existence and Uniqueness of Solutions for Non-Autonomous Complementarity Dynamical Systems. Journal of Convex Analysis, Heldermann, 2010, 17 (3&4), pp.961-990. ⟨hal-00756226⟩

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