Stratified discontinuous differential equations and sufficient conditions for robustness

Cristopher Hermosilla (1, 2)

1 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
2 OC - Optimisation et commande

This paper is concerned with state-constrained discontinuous ordinary differential equations for which the corresponding vector field has a set of singularities that forms a stratification of the state domain. Existence of solutions and robustness with respect to external perturbations of the righthand term are investigated. Moreover, notions of regularity for stratifications are discussed.

Mots clés: Existence of solutions; Stratified systems; State-constrained ODEs; Discontinuous vector fields; Robustness; State-constrained ODEs.

Domaines: Optimisation et contrôle [math.OC]

Cristopher Hermosilla. Stratified discontinuous differential equations and sufficient conditions for robustness. Discrete and Continuous Dynamical Systems - Series A, 2015, 35 (9), pp.23. ⟨10.3934/dcds.2015.35.4415⟩. ⟨hal-00955927⟩