Přístupnostní navigace
E-application
Search Search Close
Publication detail
DIBLÍK, J. SVOBODA, Z.
Original Title
Asymptotic properties of delayed matrix exponential function via Lambert function
Type
journal article in Web of Science
Language
English
Original Abstract
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.
Keywords
Lambert function, delayed matrix exponential, asymptotic behavior, principal part, instability.
Authors
DIBLÍK, J.; SVOBODA, Z.
Released
15. 1. 2018
Publisher
Americal Institute of Mathematical Sciences
ISBN
1553-524X
Periodical
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
Year of study
72
Number
10
State
United States of America
Pages from
123
Pages to
144
Pages count
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" }