Maximal monotonicity and cyclic monotonicity arising in nonsmooth Lur'e dynamical systems

Samir Adly (1) , Abderrahim Hantoute (2) , Le Ba Khiet (2)

1 XLIM-MATHIS - Mathématiques & Sécurité de l'information
2 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]

We study a precomposition of a maximal monotone operator with linear mappings, which preserves the maximal monotonicity in the setting of reflexive Banach spaces. Instead of using the adjoint of such linear operators, as in the usual precomposition, we consider a more general situation involving operators which satisfy the so-called passivity condition. We also provide similar analysis for the preservation of the maximal cyclic monotonicity. These results are applied to derive existence results for nonsmooth Lur'e dynamical systems.

Mots clés: Maximal monotonicity; Maximal cyclic monotonicity; Precomposition with linear operators; Passivity condition; Lur'e systems; Differential inclusions

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Samir Adly, Abderrahim Hantoute, Le Ba Khiet. Maximal monotonicity and cyclic monotonicity arising in nonsmooth Lur'e dynamical systems. Australian Journal of Mathematical Analysis and Applications, 2017, 448 (1), pp.691 - 706. ⟨10.1016/j.jmaa.2016.11.025⟩. ⟨hal-01656064⟩