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 Izv. IMI UdGU, 2021, Volume 57, Pages 3–76 (Mi iimi408)

MATHEMATICS

Local assignability of Lyapunov exponents of linear discrete-time system

I. N. Banshchikova

Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia

Abstract: We consider sufficient and necessary conditions for the proportional local assignability of the Lyapunov spectrum of the system
$$x(m+1)=(A(m)+B(m)U(m))x(m), \quad m\in\mathbb Z,\quad x\in\mathbb R^n.$$
The properties of stability of the Lyapunov spectrum and integral separation of linear discrete-time systems are studied, description of the spectral set of a linear system in the case of the full spectrum stability is obtained, the property of uniform complete controllability of a linear system with discrete time is studied, and the properties of the Bebutov shell of a linear discrete-time control system are investigated.

Keywords: linear discrete-time system, Lyapunov exponents, controllability, stabilizability, dynamic shift system.

 Funding Agency Grant Number Ministry of Science and Higher Education of the Russian Federation 075-00232-20-01, ïðîåêò FEWS-2020-0010 20-01-00293 This research was funded by the Ministry of Science and Higher Education of the Russian Federation in the framework of state assignment No. 075-00232-20-01, project FEWS-2020-0010, and was funded by RFBR, project number 20-01-00293.

DOI: https://doi.org/10.35634/2226-3594-2021-57-01

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Bibliographic databases:

UDC: 517.962.22, 517.977
MSC: 39A06, 39A22, 39A30, 93B55

Citation: I. N. Banshchikova, “Local assignability of Lyapunov exponents of linear discrete-time system”, Izv. IMI UdGU, 57 (2021), 3–76

Citation in format AMSBIB
\Bibitem{Ban21} \by I.~N.~Banshchikova \paper Local assignability of Lyapunov exponents of linear discrete-time system \jour Izv. IMI UdGU \yr 2021 \vol 57 \pages 3--76 \mathnet{http://mi.mathnet.ru/iimi408} \crossref{https://doi.org/10.35634/2226-3594-2021-57-01}