Existence, uniqueness of solutions and stability of nonsmooth multivalued Lur'e dynamical systems

Bernard Brogliato (1) , Daniel Goeleven (2)

1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
2 PIMENT - Physique et Ingénierie Mathématique pour l'Énergie, l'environnemeNt et le bâtimenT

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.

Domaines: Optimisation et contrôle [math.OC]

Bernard Brogliato, Daniel Goeleven. Existence, uniqueness of solutions and stability of nonsmooth multivalued Lur'e dynamical systems. Journal of Convex Analysis, 2013, 20 (3), pp.881-900. ⟨hal-00825601⟩