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November  2014, 34(11): 4577-4588. doi: 10.3934/dcds.2014.34.4577

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

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

Received  October 2013 Revised  January 2014 Published  May 2014

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.
Citation: Jan Čermák, Jana Hrabalová. Delay-dependent stability criteria for neutral delay differential and difference equations. Discrete & Continuous Dynamical Systems, 2014, 34 (11) : 4577-4588. doi: 10.3934/dcds.2014.34.4577
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