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On matrix differential equations with several unbounded delays

Published online by Cambridge University Press:  25 July 2006

J. ĈERMÁK
Affiliation:
Institute of Mathematics, Brno University of Technology, Technická 2, 616 69 Brno, Czech Republic email: cermak.j@fme.vutbr.cz

Abstract

The paper focuses on the matrix differential equation \[ \dot y(t)=A(t)y(t)+\sum_{j=1}^{m}B_j(t)y(\tau_j(t))+f(t),\quad t\in I=[t_0,\infty)\vspace*{-3pt} \] with continuous matrices $A$, $B_j$, a continuous vector $f$ and continuous delays $\tau_j$ satisfying $\tau_k\circ\tau_l =\tau_l\circ\tau_k$ on $I$ for any pair $\tau_k,\tau_l$. Assuming that the equation \[ \dot y(t)=A(t)y(t)\] is uniformly exponentially stable, we present some asymptotic bounds of solutions $y$ of the considered delay equation. A system of simultaneous Schröder equations is used to formulate these asymptotic bounds.

Type
Papers
Copyright
2006 Cambridge University Press

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