# American Institute of Mathematical Sciences

September  2015, 35(9): 4415-4437. doi: 10.3934/dcds.2015.35.4415

## Stratified discontinuous differential equations and sufficient conditions for robustness

 1 Project Commands INRIA Saclay & ENSTA ParisTech, 828, Boulevard des Maréchaux, 91762 Palaiseau, France

Received  March 2014 Published  April 2015

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.
Citation: Cristopher Hermosilla. Stratified discontinuous differential equations and sufficient conditions for robustness. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4415-4437. doi: 10.3934/dcds.2015.35.4415
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