Publication detail

# Asymptotic properties of delayed matrix exponential function via Lambert function

DIBLÍK, J. SVOBODA, Z.

Original Title

Asymptotic properties of delayed matrix exponential function via Lambert function

English Title

Asymptotic properties of delayed matrix exponential function via Lambert function

Type

journal article in Web of Science

Language

en

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.

English 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.

Released

15.01.2018

Publisher

Americal Institute of Mathematical Sciences

ISBN

1553-524X

Periodical

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

Year of study

72

Number

10

State

US

Pages from

123

Pages to

144

Pages count

22

URL

Documents

BibTex

```
@article{BUT150426,
author="Josef {Diblík} and Zdeněk {Svoboda}",
title="Asymptotic properties of delayed matrix exponential function via Lambert function",
annote="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.",
address="Americal Institute of Mathematical Sciences",
chapter="150426",
doi="10.3934/dcdsb.2018008",
howpublished="print",
institution="Americal Institute of Mathematical Sciences",
number="10",
volume="72",
year="2018",
month="january",
pages="123--144",
publisher="Americal Institute of Mathematical Sciences",
type="journal article in Web of Science"
}
```