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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2023, Volume 321, Pages 162–171
DOI: https://doi.org/10.4213/tm4313 (Mi tm4313) 		 
On the Length of Switching Intervals of a Stable Dynamical System

Rinat A. Kamalova, Vladimir Yu. Protasovbc

a Moscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701 Russia
b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119991 Russia
c University of L'Aquila, piazza Santa Margherita 2, 67100 L'Aquila, Italy
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DOI: https://doi.org/10.4213/tm4313
Abstract: A linear switching system is a system of linear ODEs with time-dependent matrix taking values in a given control matrix set. The system is asymptotically stable if all its trajectories tend to zero for every control matrix function. Mode-dependent restrictions on the lengths of switching intervals can be imposed. Does the system remain stable after removal of the restrictions? When does the stability of the trajectories with short switching intervals imply the stability of all trajectories? The answers to these questions are given in terms of the “tail cut-off points” of linear operators. We derive an algorithm to compute them by applying Chebyshev-type exponential polynomials.
Keywords: linear switching system, dynamical system, stability, switching time intervals, quasipolynomials, extremal polynomial, Chebyshev system, convex extremal problem.
Funding agency Grant number
Foundation for the Development of Theoretical Physics and Mathematics BASIS
This work is supported by the Theoretical Physics and Mathematics Advancement Foundation “BASIS.”
Received: July 30, 2022
Revised: October 29, 2022
Accepted: December 13, 2022
English version:
Proceedings of the Steklov Institute of Mathematics, 2023, Volume 321, Pages 149–157
DOI: https://doi.org/10.1134/S0081543823020116
Bibliographic databases:
Document Type: Article
UDC: 517.518.862+517.537.7+517.929.21+517.587
Language: Russian
Citation: Rinat A. Kamalov, Vladimir Yu. Protasov, “On the Length of Switching Intervals of a Stable Dynamical System”, Optimal Control and Dynamical Systems, Collected papers. On the occasion of the 95th birthday of Academician Revaz Valerianovich Gamkrelidze, Trudy Mat. Inst. Steklova, 321, Steklov Math. Inst., Moscow, 2023, 162–171; Proc. Steklov Inst. Math., 321 (2023), 149–157
Citation in format AMSBIB
\Bibitem{KamPro23}
\by Rinat~A.~Kamalov, Vladimir~Yu.~Protasov
\paper On the Length of Switching Intervals of a Stable Dynamical System
\inbook Optimal Control and Dynamical Systems
\bookinfo Collected papers. On the occasion of the 95th birthday of Academician Revaz Valerianovich Gamkrelidze
\serial Trudy Mat. Inst. Steklova
\yr 2023
\vol 321
\pages 162--171
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4313}
\crossref{https://doi.org/10.4213/tm4313}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2023
\vol 321
\pages 149--157
\crossref{https://doi.org/10.1134/S0081543823020116}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85170839630}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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