Almost complete controllability of linear autonomous difference-differential systems of neutral type

Abstract

For linear autonomous systems of neutral type with absolutely continuous initial states, it is shown that the spectral condition $$ rank[\lambda E - D - e^{ - \lambda h} (D_1 + D_2 \lambda ),B] = n \forall \lambda \in \mathbb{C} $$ is necessary and sufficient for the controllability of “almost all” initial states to zero. Considerations have a constructive nature. The results are illustrated by an example.