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Controllability conditions of linear singularly perturbed systems with small state and input delays

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Abstract

A singularly perturbed linear time-dependent controlled system with a point-wise delay in state and control variables is considered. The delay is 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. 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 proper kinds of controllability of the slow and fast subsystems yield the complete Euclidean 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.

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Authors and Affiliations

  1. Department of Applied Mathematics, Ort Braude College of Engineering, 51 Snunit Str., P.O.B. 78, Karmiel, 2161002, Israel

    Valery Y. Glizer

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  1. Valery Y. Glizer
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Correspondence to Valery Y. Glizer.

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Glizer, V.Y. Controllability conditions of linear singularly perturbed systems with small state and input delays. Math. Control Signals Syst. 28, 1 (2016). https://doi.org/10.1007/s00498-015-0152-3

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