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Journal of Convex Analysis 20 (2013), No. 3, 881--900
Copyright Heldermann Verlag 2013

Existence, Uniqueness of Solutions and Stability of Nonsmooth Multivalued Lur'e Dynamical Systems

Bernard Brogliato
INRIA, ZIRST Montbonnot, 655 Avenue de l'Europe, 38334 Saint Ismier, France

Daniel Goeleven
PIMENT, Université de La Réunion, 97400 Saint-Denis, France

This paper deals with the well-posedness of a class of multivalued Lur'e systems, which consist of a nonlinear dynamical system in negative feedback interconnection with a static multivalued nonlinearity. The objective is to provide a detailed analysis of the conditions which guarantee that a certain operator, constructed from the static nonlinearity, is maximal monotone. This in turn assures the existence and the uniqueness of the solutions. Examples (nonlinear complementarity systems, nonlinear relay systems) illustrate the developments. A stability result is also given.

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