Delay-dependent stability conditions for fundamental characteristic functions

Abstract

. This paper is devoted to the investigation on the stability for two characteristic functions f 1 ( z ) = z 2 + pe − zτ + q and f 2 ( z ) = z 2 + pze − zτ + 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.