Asymptotic Behavior of the Delayed Matrix Exponential Function

Asymptotic Behavior of the Delayed Matrix Exponential Function

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The paper discusses asymptotic behaviors of the delayed matrix exponential, delayed matrix sine and delayed matrix cosine. Such functions were defined in connection with a formalization of the step method for linear systems of differential equations with a constant delay r. The above matrix functions are defined by matrix polynomials on every interval [(k − 1)τ, kτ), where k = 0, 1, . . . and τ > 0. To investigate the asymptotic behavior of the delayed matrix functions, the main branch of the Lambert function is used.

The paper discusses asymptotic behaviors of the delayed matrix exponential, delayed matrix sine and delayed matrix cosine. Such functions were defined in connection with a formalization of the step method for linear systems of differential equations with a constant delay r. The above matrix functions are defined by matrix polynomials on every interval [(k − 1)τ, kτ), where k = 0, 1, . . . and τ > 0. To investigate the asymptotic behavior of the delayed matrix functions, the main branch of the Lambert function is used.

asymptotic behavior; delayed matrix exponential; delayed matrix sine; delayed matrix cosine; Lambert function

asymptotic behavior; delayed matrix exponential; delayed matrix sine; delayed matrix cosine; Lambert function

SVOBODA, Z.; DIBLÍK, J.

2019

21.07.2018

American Institute of Physics

AMER INST PHYSICS, 2 HUNTINGTON QUADRANGLE, STE 1NO1, MELVILLE, NY 11747-4501 USA

978-0-7354-1690-1

INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017)

0094-243X

AIP conference proceedings

Spojené státy americké

430006-1

430006-4

4

https://doi.org/10.1063/1.5044021