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Title: Stability and stabilization of one class of three time-scale systems with delays (English)
Author: Glizer, Valery Y.
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 58
Issue: 4
Year: 2022
Pages: 593-625
Summary lang: English
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Category: math
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Summary: A singularly perturbed linear time-invariant time delay controlled system is considered. The singular perturbations are subject to the presence of two small positive multipliers for some of the derivatives in the system. These multipliers (the parameters of singular perturbations) are of different orders of the smallness. The delay in the slow state variable is non-small (of order of $1$). The delays in the fast state variables are proportional to the corresponding parameters of singular perturbations. Three much simpler parameters-free subsystems are associated with the original system. It is established that the exponential stability of the unforced versions of these subsystems yields the exponential stability of the unforced version of the original system uniformly in the parameters of singular perturbations. It also is shown that the stabilization of the parameters-free subsystems by memory-free state-feedback controls yields the stabilization of the original system by a memory-free state-feedback control uniformly in the parameters of singular perturbations. Illustrative examples are presented. (English)
Keyword: linear controlled system
Keyword: time delay system
Keyword: three time-scale singularly perturbed system
Keyword: exponential stability
Keyword: memory-free state-feedback stabilization
MSC: 93C23
MSC: 93C70
MSC: 93D15
MSC: 93D23
idZBL: Zbl 07655849
idMR: MR4521858
DOI: 10.14736/kyb-2022-4-0593
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Date available: 2022-12-02T13:18:38Z
Last updated: 2023-10-04
Stable URL: http://hdl.handle.net/10338.dmlcz/151167
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