Numerical Stability Test of Neutral Delay Differential Equations

The stability of a delay differential equation can be investigatedon the basis of the root location of the characteristic function. Though a number of stabilitycriteria are available, they usually do not provide any information about the characteristic rootwith maximal real part, which is useful in justifying the stability and in understanding the systemperformances. Because the characteristic function is a transcendental function that has an infinitenumber of roots with no closed form, the roots can be found out numerically only. While someiterative methods work effectively in finding a root of a nonlinear equation for a properly choseninitial guess, they do not work in finding the rightmost root directly from the characteristic function.On the basis of Lambert W function, this paper presents an effective iterative algorithm for the calculationof the rightmost roots of neutral delay differential equations so that the stability of the delay equationscan be determined directly, illustrated with two examples