On the notion of strong relative degree and its implications on the design of extended PD-controllers for time-delay systems*

The fundamental notion of relative degree is studied for a class of linear time-delay systems of retarded type, where the standard assumption of commensurate delays is dropped. Even though the analyzed systems do not have a non-trivial feedthrough from input to output, it is shown that the relative degree may be sensitive to infinitesimal delay perturbations. This observation is at the basis of a novel notion of relative degree, called strong relative degree, which is characterized algebraically and computationally. It plays a key role in guaranteeing well-posedness of systems controlled with extended PD controllers, for which a design procedure and numerical experiments are presented.