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

Valery Y. Glizer

doi:10.3934/naco.2020027

Article Contents

2021, Volume 11, Issue 2: 307-320. Doi: 10.3934/naco.2020027

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

Valery Y. Glizer

Department of Applied Mathematics, ORT Braude College of Engineering, Karmiel, Israel, and, Independent Center for Studies, in Control Theory and Applications, Haifa, Israel

Received: July 31, 2019

Revised: February 29, 2020

Early access: May 2020

Published: June 2021

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Abstract

A singularly perturbed linear time-dependent controlled system with a point-wise nonsmall (of order of $ 1 $) 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.

Keywords:

Controlled system,
input delay,
singular perturbation,
parameter-dependent controllability matrix,
asymptotic analysis,
parameter-free controllability conditions.

Mathematics Subject Classification: Primary:34K26, 93B05, 93C23;Secondary:65F40.

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References

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