Stability switches in a class of characteristic equations with delay-dependent parameters

In this paper, a method for determining the stability of the characteristic equation P(lambda, T) + Q(lambda, T)e(-lambdaT) + R(lambda, T)e(-2lambda7) = 0 is introduced. By this method, the purely imaginary eigenvalues can be found and the crossing direction of the eigenvalues through the imaginary axis as the delay T increases can be determined by a simple formula. The results show that stability switches may occur and the ultimate situation may be stable, unstable or alternately switching forever. (C) 2003 Elsevier Ltd. All rights reserved.