T-Accessibility for a class of nonlinear time–delay systems

Observability and detectability on one hand as well as accessibility and controllability on the other, are related properties and have not been closely investigated for nonlinear–time delay systems until these recent years. Currently accessibility or nonlinear time delay systems is defined as the absence of autonomous functions on the extended state space. Such a property is expressed in terms of the Accessibility matrix rank, extending to the nonlinear context the well known Kalman Criterion. A weaker notion is introduced in this paper which is motivated by the fact that even if autonomous functions exist for the given system, it may be still possible to move from a fixed point to an arbitrary one in some open subset of IRn. The study is performed on the class of driftless single input systems