Delay-dependent stability conditions for fundamental characteristic functions

This paper is devoted to the investigation on 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 $p$ $q$ are real numbers $\tau >0$. The obtained theorems describe explicit dependence changing delay $. Our results applied some special cases of a linear differential system with in diagonal terms delay-dependent conditions obtained.