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Delay-dependent stability conditions for fundamental characteristic functions

Hideaki Matsunaga (2023)

Archivum Mathematicum

This paper is devoted to the investigation on the stability for two characteristic functions f 1 ( z ) = z 2 + p e - z τ + q and f 2 ( z ) = z 2 + p z e - z τ + q , where p and q are real numbers and τ > 0 . The obtained theorems describe the explicit stability dependence on the changing delay τ . 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.

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