Stabilizability Conditions for One Class of Linear Singularly Perturbed Differential-Difference Systems

Asingularly perturbed linear time-invariant controlled system with a point-wise delay in the state variables is considered. The delay is nonsmall. It appears in both, slow and fast, state variables but only in the slow mode equation. Two much simpler parameter-free subsystems (the slow and fast ones) are associated with this system. Although the original singularly perturbed system has the delay only in the state variables, its slow subsystem has delays in both, state and control, variables. It is established in the paper that the stabilizability of the slow and fast subsystems yields the stabilizability of the original singularly perturbed system for all sufficiently small values of the parameter of singular perturbation. The theoretical results are illustrated by example.