Summary: In this paper, a non-autonomous differential system with state delays and with a large coefficient for the control (high gain control) is considered. By a proper control transformation, this system is converted into equivalent time delay system singularly perturbed by a small positive parameter. The latter system, is decomposed asymptotically into two much simpler parameter-free subsystems, slow and fast ones. The slow subsystem has delays in the state and control variables, while the fast subsystem is delay-free. Based on the assumption of the Euclidean space controllability of the slow subsystem, the Euclidean space controllability of the transformed and original systems is established for all sufficiently small values of the parameter of singular perturbation.
Also, the minimum energy control problem for the transformed system is considered. Asymptotic behaviour with respect to the small parameter of the solution to this problem is studied. An illustrative example is presented.