Lyapunov pairs for perturbed sweeping processes

Abderrahim Hantoute (1) , Emilio Vilches (2, 3, 4)

1 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]
2 DIM - Departamento de Ingeniería Matemática [Santiago]
3 ICEd - UOH - Instituto de Ciencias de la educacion
4 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We give a full characterization of nonsmooth Lyapunov pairs for perturbed sweeping processes under very general hypotheses. As a consequence, we provide an existence result and a criterion for weak invariance for perturbed sweeping processes. Moreover, we characterize Lyapunov pairs for gradient complementarity dynamical systems.

Mots clés: Sweeping process; Lyapunov pair; Differential inclusions; Invariance; Normal cone; Complementarity dynamical systems

Domaines: Mathématiques [math]; Systèmes dynamiques [math.DS]

Abderrahim Hantoute, Emilio Vilches. Lyapunov pairs for perturbed sweeping processes. Optimization Letters, 2018, 12, pp.1773-1787. ⟨10.1007/s11590-018-1231-4⟩. ⟨hal-01801628⟩