Realization of time-delay systems

The paper addresses the problem of transforming a single-input single-output nonlinear retarded time-delay system, described by an input-output equation, in the traditional observable state space form. The solution is generalized from the delay-free case and depends on integrability of certain submodule of differential 1-forms. The integrability conditions are improved to make them constructive. Finally, it is explained why one may obtain two realizations, which are not connected by bi-causal change of state coordinates.