Approximate state-space controllability of linear singularly perturbed systems with two scales of state delays

Article type: Research Article

Authors: Glizer, Valery Y.

Affiliations: Department of Mathematics, ORT Braude College of Engineering, 51 Snunit Str., P.O.B. 78, Karmiel 2161002, Israel. E-mails: [email protected], [email protected]; Tel.: 972-4-9901801; Fax: 972-4-9901802

Abstract: A singularly perturbed linear time-dependent controlled system with multiple point-wise and distributed state delays is considered. The delays in the fast state variable are small of order of the small positive multiplier for a part of the derivatives in the system, which is a parameter of the singular perturbation. The delays in the slow state variable are non-small. Two types of the original singularly perturbed system, standard and nonstandard, are analyzed. For each type, two much simpler parameter-free subsystems (the slow and fast ones) are associated with the original system. It is established in the paper that the approximate state-space controllability of the slow and fast subsystems yields the approximate state-space controllability of the original system robustly with respect to the parameter of singular perturbation for all its sufficiently small values. Illustrative examples are presented.

Keywords: Singularly perturbed system, state delay, approximate state-space controllability

DOI: 10.3233/ASY-171451

Journal: Asymptotic Analysis, vol. 107, no. 1-2, pp. 73-114, 2018