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Avtomatika i Telemekhanika, 2019, Issue 12, Pages 24–46
DOI: https://doi.org/10.1134/S000523101912002X (Mi at14826) 		 
Linear Systems

Robust stability of linear periodic systems

S. V. Kravchuka, V. I. Slyn'kob

a Bohdan Khmelnytsky National University of Cherkasy, Cherkasy, Ukraine
b University of Würzburg, Institute of Mathematics, Würzburg, Germany
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DOI: https://doi.org/10.1134/S000523101912002X
Abstract: A new method for analyzing the robust stability of linear periodic systems is proposed, which is based on the ideas of commutator calculus in combination with Lyapunov’s direct method. The stability analysis of a linear nonautonomous system of ordinary differential equations is reduced to the stability analysis of a linear system of differential equations with impulse action, for which Lyapunov’s direct method is used. New sufficient conditions for the robust stability of a linear periodic system with non-periodic perturbations are established. Some illustrative examples on the robust stability analysis of linear systems are given.
Keywords: robust stability, linear periodic systems, Lyapunov’s direct method, commutator calculus, Magnus series.
Funding agency Grant number
Ministry of Education and Science of Ukraine 0116U004691
National Academy of Sciences of Ukraine 6541230
This work was supported in part by the Ministry of Education and Science of Ukraine, project no. 0116U004691, and in part by the National Academy of Sciences of Ukraine within budgetary program no. 6541230 “Supporting the Development of Priority Lines of Research.”
Presented by the member of Editorial Board: P. S. Shcherbakov

Received: 14.07.2017
Revised: 19.04.2019
Accepted: 24.05.2019
English version:
Automation and Remote Control, 2019, Volume 80, Issue 12, Pages 2108–2125
DOI: https://doi.org/10.1134/S0005117919120026
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. V. Kravchuk, V. I. Slyn'ko, “Robust stability of linear periodic systems”, Avtomat. i Telemekh., 2019, no. 12, 24–46; Autom. Remote Control, 80:12 (2019), 2108–2125
Citation in format AMSBIB
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