Euclidean Space Controllability Conditions of Singularly Perturbed Systems with Multiple State and Control Delays

A singularly perturbed linear time-dependent system with multiple point-wise and distributed delays in the state and control is considered. The state delays are of two scales (nonsmall and small), while the control delays are small. The small delays are of order of a small positive multiplier for a part of the derivatives in the system which is a parameter of the singular perturbation. Two much simpler parameter-free subsystems (the slow and fast ones) are associated with the original system. It is established that, subject to proper assumptions, the complete Euclidean space controllability of the slow and fast subsystems yields the complete Euclidean space controllability of the original system robust with respect to the parameter of singular perturbation for all its sufficiently small values. An illustrative example is presented.