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

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


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