**Olga Tsekhan**

Faculty of Economics and Management, Yanka Kupala State University of Grodno, 230023 Grodno, Belarus; tsekhan@grsu.by

Received: 19 February 2019; Accepted: 23 May 2019; Published: 3 June 2019

**Abstract:** The problem of complete controllability of a linear time-invariant singularly-perturbed system with multiple commensurate non-small delays in the slow state variables is considered. An approach to the time-scale separation of the original singularly-perturbed system by means of Chang-type non-degenerate transformation, generalized for the system with delay, is used. Sufficient conditions for complete controllability of the singularly-perturbed system with delay are obtained. The conditions do not depend on a singularity parameter and are valid for all its sufficiently small values. The conditions have a parametric rank form and are expressed in terms of the controllability conditions of two systems of a lower dimension than the original one: the degenerate system and the boundary layer system.

**Keywords:** time delay system; multiple commensurate delays; singular perturbation; decomposition; Chang transformation; complete controllability; robust sufficient condition
