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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2019, Volume 29, Issue 1, Pages 40–51 (Mi vuu664)  

This article is cited in 3 scientific papers (total in 3 papers)

MATHEMATICS

The structure of the Cauchy operator to a linear continuous-discrete functional differential system with aftereffect and some properties of its components

V. P. Maksimov

Perm State National Research University, ul. Bukireva, 15, Perm, 614990, Russia

Abstract: In this paper, a class of linear functional differential systems with aftereffect, continuous and discrete times, and impulses (impulse hybrid systems) is considered. The focus of attention is on the structure of the Cauchy operator to the hybrid system under consideration and the representation of their components. Those allow one to give the representation of all trajectories of the hybrid system and to formulate conditions of the solvability for control problems in various classes of controls, to obtain estimates of the attainability sets under constrained control, and to study general linear boundary value problems for the solvability. A detailed description of all components to the Cauchy operator is given and their properties are studied. For the components with continuous time, some conditions of the continuity with respect to the second argument are obtained which is related to deciding on a class of controls. The main results are based on constructions of the Cauchy matrices to systems with continuous time and difference systems.

Keywords: linear systems with delay, functional differential systems with continuous and discrete times, representation of solutions, Cauchy operator.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00332_а
The research was supported by the Russian Foundation for Basic Research (project no. 18-01-00332).


DOI: https://doi.org/10.20537/vm190104

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Bibliographic databases:

UDC: 517.929
MSC: 34K10, 34K30, 34K35, 91B74
Received: 01.02.2019
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Citation: V. P. Maksimov, “The structure of the Cauchy operator to a linear continuous-discrete functional differential system with aftereffect and some properties of its components”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:1 (2019), 40–51

Citation in format AMSBIB
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\by V.~P.~Maksimov
\paper The structure of the Cauchy operator to a linear continuous-discrete functional differential system with aftereffect and some properties of its components
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2019
\vol 29
\issue 1
\pages 40--51
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\crossref{https://doi.org/10.20537/vm190104}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. P. Maksimov, “On a class of linear continuous-discrete systems with discrete memory”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:3 (2020), 385–395  mathnet  crossref
    2. E. Bravyi, V. Maksimov, P. Simonov, “Some economic dynamics problems for hybrid models with aftereffect”, Mathematics, 8:10 (2020), 1832  crossref  isi  scopus
    3. V. P. Maksimov, “O vnutrennikh otsenkakh mnozhestv dostizhimosti dlya nepreryvno-diskretnykh sistem s diskretnoi pamyatyu”, Tr. IMM UrO RAN, 27, no. 3, 2021, 141–151  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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