Towards integrability for nonlinear time-delay systems

In this paper the integrability of differential one-forms is studied in case time-delays are present. Two notions, weak and strong integrability, are defined and the difference with delay-free case is explained. After giving the algorithms to check if some one-forms are strongly or weakly integrable, based on examples, the differences of the two notions of integrability are studied. Finally, the role of integrability is explained when looking for a change of coordinates together with an application to accessibility property