Prediction-free tracking control for systems with incommensurate lumped and distributed delays: Two examples*

Linear systems with lumped and distributed delays can be represented by modules over the ring of entire functions in Ĉ(s)[e–τs]. While in the case of commensurate delays spectral controllability is sufficient for the existence of a basis of this module, in the incommensurate case addressed here additional conditions are required. Exploiting the relations between the (known) delay amplitudes a new module with favorable freeness properties can be defined. Based on that, necessary and sufficient conditions for the freeness of this module are presented. If these conditions are satisfied a basis can be used to derive a flatness-based tracking control without any explicit predictions. The approach is illustrated on a neutral system and on a system with distributed delays.