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Euclidean space output controllability of singularly perturbed systems with small state delays

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Abstract

A singularly perturbed linear time-dependent controlled system with multiple pointwise and distributed delays in the state variables is considered. The state delays 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. Along with the dynamic system, a linear algebraic delay-free output equation is considered. Two much simpler parameter-free subsystems (the slow and fast ones) are associated with the original system. It is established that proper kinds of controllability of the slow and fast subsystems yield the Euclidean space output controllability of the original system robust with respect to the parameter of singular perturbation for all its sufficiently small values. Illustrative examples are presented.

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  1. Department of Applied Mathematics, ORT Braude College of Engineering, P.O. Box 78, Karmiel, 2161002, Israel

    Valery Y. Glizer

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Glizer, V.Y. Euclidean space output controllability of singularly perturbed systems with small state delays. J. Appl. Math. Comput. 57, 1–38 (2018). https://doi.org/10.1007/s12190-017-1092-5

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