Delay-dependent stability criteria for neutral delay differential and difference equations

Jan Čermák; Jana Hrabalová

doi:10.3934/dcds.2014.34.4577

Article Contents

2014, Volume 34, Issue 11: 4577-4588. Doi: 10.3934/dcds.2014.34.4577

This issue Previous Article On ill-posedness for the generalized BBM equation Next Article Integrability of Hamiltonian systems with homogeneous potentials of degrees $\pm 2$. An application of higher order variational equations

Delay-dependent stability criteria for neutral delay differential and difference equations

Jan Čermák^1, and
Jana Hrabalová^1,

1.
Institute of Mathematics, Brno University of Technology, Technická 2, CZ-61669 Brno

Received: September 30, 2013

Revised: December 31, 2013

Published: October 2014

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Abstract

This paper discusses asymptotic stability properties of the neutral delay differential equation \begin{eqnarray*} y'(t) = a y (t) + b y ( t - \tau ) + c y'( t - \tau ), t > 0, \\ \end{eqnarray*} where $a,\,b,\,c$ and $\tau >0$ are real scalars. We consider the exact as well as discretized delay-dependent asymptotic stability regions for this equation and describe them in terms of explicit necessary and sufficient conditions imposed on $a,\,b,\,c$ and $\tau$. Such descriptions enable us to observe some fundamental properties of these stability regions, especially with respect to stability of corresponding numerical formulae. As a consequence of our investigations, we extend existing results on this topic.

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Mathematics Subject Classification: Primary: 34K20, 39A30; Secondary: 34K28, 39A12, 65L20.

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