On pointwise controllability of a linear time-invariant singularly perturbed system with delay

Different notions of pointwise controllability are introduced, compared and analyzed for a linear time-invariant singularly perturbed system with state delay. These notions differ in the dependence of the terminal time and control on the small parameter, the boundedness of the control, and the accuracy of hitting prescribed points. A hierarchy of the introduced notions is established. The structure of the pointwise controllability operator is revealed, which justifies the relationship between robust and $\mu$-uniform controllability. Sufficient decomposition conditions for robust controllability, expressed in terms of the controllability matrices of the slow and fast subsystems, are proved. The theoretical results are illustrated by examples.