Novel Conditions of Euclidean space controllability for singularly perturbed systems with input delay

Abstract

<p style='text-indent:20px;'>A singularly perturbed linear time-dependent controlled system with a point-wise nonsmall (of order of <inline-formula><tex-math id="M1">\begin{document}$ 1 $\end{document}</tex-math></inline-formula>) delay in the input (the control variable) is considered. Sufficient conditions of the complete Euclidean space controllability for this system, robust with respect to the parameter of singular perturbation, are derived. This derivation is based on an asymptotic analysis of the controllability matrix for the considered system and on such an analysis of the determinant of this matrix. However, this derivation does not use a slow-fast decomposition of the considered system. The theoretical result is illustrated by an example.