Geodesic
Delay-dependent stability conditions for fundamental characteristic functions
Archivum mathematicum, Tome 59 (2023) no. 1, pp. 77-84

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This paper is devoted to the investigation on the stability for two characteristic functions $f_1(z) = z^2+pe^{-z\tau }+q$ and $f_2(z) = z^2+pz e^{-z\tau }+q$, where $p$ and $q$ are real numbers and $\tau >0$. The obtained theorems describe the explicit stability dependence on the changing delay $\tau $. Our results are applied to some special cases of a linear differential system with delay in the diagonal terms and delay-dependent stability conditions are obtained.
DOI : 10.5817/AM2023-1-77
Classification : 34K20, 34K25
Keywords: characteristic equation; delay; stability switch 
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Matsunaga, Hideaki. Delay-dependent stability conditions for fundamental characteristic functions. Archivum mathematicum, Tome 59 (2023) no. 1, pp. 77-84. doi: 10.5817/AM2023-1-77

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