Geodesic
Existence and Uniqueness of Solutions for Non-Autonomous Complementarity Dynamical Systems
Journal of convex analysis, Tome 17 (2010) no. 3, pp. 961-99

Voir la notice de l'article provenant de la source Heldermann Verlag

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 "input-output" 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 by J. F. Edmond and L. Thibault ["Relaxation of an optimal control problem involving a perturbed sweeping process", Mathematical Programming 104 (2005) 347--373; and "BV solutions of nonconvex sweeping process differential inclusions with perturbation", Journal of Differential Equations 226 (2006) 135--179] and L. Thibault ["Sweeping process with regular and nonregular sets", Journal of Differential Equations, 193 (2003) 1--26] 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.
Mots-clés : Moreau's sweeping process, complementarity system, differential inclusion, existence, uniqueness, prox-regular set, state jumps, bounded variation 
@article{JCA_2010_17_3_JCA_2010_17_3_a14,
     author = {B. Brogliato and L. Thibault},
     title = {Existence and {Uniqueness} of {Solutions} for {Non-Autonomous} {Complementarity} {Dynamical} {Systems}},
     journal = {Journal of convex analysis},
     pages = {961--99},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2010},
     url = {http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a14/}
}
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B. Brogliato; L. Thibault. Existence and Uniqueness of Solutions for Non-Autonomous Complementarity Dynamical Systems. Journal of convex analysis, Tome 17 (2010) no. 3, pp. 961-99. http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a14/