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DIBLÍK, J. SVOBODA, Z.
Originální název
Asymptotic properties of delayed matrix exponential function via Lambert function
Typ
článek v časopise ve Web of Science, Jimp
Jazyk
angličtina
Originální abstrakt
In the case of first-order linear systems with single constant delay and with constant matrix, the application of the well-known step by step method (when ordinary diffrential equations with delay are solved) has recently been formalized using a special type matrix, called delayed matrix exponential. In the paper, the asymptotic properties of delayed matrix exponential are studied for and it is, e.g., proved that the sequence of values of a delayed matrix exponential at nodes is approximately represented by a geometric progression. A constant matrix has been found such that its matrix exponential is the quotient factor that depends on the principal branch of the Lambert function. Applications of the results obtained are given as well.
Klíčová slova
Lambert function, delayed matrix exponential, asymptotic behavior, principal part, instability.
Autoři
DIBLÍK, J.; SVOBODA, Z.
Vydáno
15. 1. 2018
Nakladatel
Americal Institute of Mathematical Sciences
ISSN
1553-524X
Periodikum
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
Ročník
72
Číslo
10
Stát
Spojené státy americké
Strany od
123
Strany do
144
Strany počet
22
URL
http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14696
BibTex
@article{BUT150426, author="Josef {Diblík} and Zdeněk {Svoboda}", title="Asymptotic properties of delayed matrix exponential function via Lambert function", journal="DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B", year="2018", volume="72", number="10", pages="123--144", doi="10.3934/dcdsb.2018008", issn="1553-524X", url="http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14696" }