B. G. Grebenshchikov, S. I. Novikov, “Instability of systems with linear delay reducible to singularly perturbed ones”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, Number 2,Pages <nobr>3

This article is cited in 13 papers

Instability of systems with linear delay reducible to singularly perturbed ones

B. G. Grebenshchikov^a, S. I. Novikov^b

^a Chair of Theoretical Mechanics, Ural State University, Ekaterinburg, Russia
^b Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, Ekaterinburg, Russia

Abstract: We investigate the stability of linear systems of differential equations with linear delay in the case when one of subsystems is singular. We establish sufficient conditions for the instability of solutions to such systems. We solve the considered problem with the help of the Laplace transformation.

Keywords: instability, functional-difference equation, Laplace transformation, asymptotic representation, meromorphic vector function.

UDC: 517.929

Received: 30.10.2007
Revised: 17.03.2008