Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2021, Volume 190, Pages 93–106
DOI: https://doi.org/10.36535/0233-6723-2021-190-93-106 (Mi into754) 		 
On the invariance of trajectories under perturbations in linear dynamic control systems

S. P. Zubovaa, E. V. Raetskayab, L. Chungc

a Voronezh State University
b Voronezh State University of Forestry and Technologies named after G.F. Morozov
c The University of Danang
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DOI: https://doi.org/10.36535/0233-6723-2021-190-93-106
Abstract: For a linear, nonstationary, completely controllable dynamical system with multipoint conditions on the state, we consider a problem on the independence of the state (trajectory) of the system of external perturbations and possible changes in the parameters of the system (internal perturbations). The problem is to construct a control for the perturbed system under which the state of the perturbed system is identical to the state of the unperturbed system. We compare controls for the unperturbed and perturbed systems at the same states of the systems.
Keywords: linear dynamical system, control, perturbation, invariance, blocking, cascade decomposition method.
Funding agency Grant number
Foundation of Development of Science and Technology of the Ministry of Education and Training of Vietnam B2017.DNA.09
This work was supported by the Foundation of Development of Science and Technology of the Ministry of Education and Training of Vietnam (project No. B2017.DNA.09).
English version:
Journal of Mathematical Sciences (New York), 2025, Volume 288, Issue 1, Pages 92–105
DOI: https://doi.org/10.1007/s10958-025-07668-6
Bibliographic databases:
Document Type: Article
UDC: 517.518
MSC: 34H05
Language: Russian
Citation: S. P. Zubova, E. V. Raetskaya, L. Chung, “On the invariance of trajectories under perturbations in linear dynamic control systems”, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 190, VINITI, Moscow, 2021, 93–106; J. Math. Sci. (N. Y.), 288:1 (2025), 92–105
Citation in format AMSBIB
\Bibitem{ZubRaeChu21}
\by S.~P.~Zubova, E.~V.~Raetskaya, L.~Chung
\paper On the invariance of trajectories under perturbations in linear dynamic control systems
\inbook Proceedings of the Voronezh spring mathematical school
“Modern methods of the theory of boundary-value problems. Pontryagin
readings – XXX”.
Voronezh, May 3-9, 2019. Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 190
\pages 93--106
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into754}
\crossref{https://doi.org/10.36535/0233-6723-2021-190-93-106}
\elib{https://elibrary.ru/item.asp?id=46675384}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2025
\vol 288
\issue 1
\pages 92--105
\crossref{https://doi.org/10.1007/s10958-025-07668-6}
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