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Axioms 2019, 8(1), 36; https://doi.org/10.3390/axioms8010036

Euclidean Space Controllability Conditions for Singularly Perturbed Linear Systems with Multiple State and Control Delays

Department of Mathematics, ORT Braude College of Engineering, Karmiel 2161002, Israel
Received: 3 February 2019 / Revised: 13 March 2019 / Accepted: 17 March 2019 / Published: 21 March 2019
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Abstract

A singularly perturbed linear time-dependent controlled system with multiple point-wise delays and distributed delays in the state and control variables is considered. The delays are small, of order of a small positive multiplier for a part of the derivatives in the system. This multiplier is a parameter of the singular perturbation. Two types of the considered 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 proper kinds of controllability of the slow and fast subsystems yield the complete Euclidean space controllability of the original system for all sufficiently small values of the parameter of singular perturbation. Illustrative examples are presented. View Full-Text
Keywords: singularly perturbed system; multiple state and control delays; controllability singularly perturbed system; multiple state and control delays; controllability
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Glizer, V.Y. Euclidean Space Controllability Conditions for Singularly Perturbed Linear Systems with Multiple State and Control Delays. Axioms 2019, 8, 36.

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