Stability conditions for the general linear difference-differential equation with constant coefficients and one constant delay (Q1823378)

In the last few years great attention has been paid to stability independent of delays. The author derives sufficient lag-independent stability conditions for all systems up to degree two inclusive. Some necessary stability conditions for large lags are expounded. In the non- neutral case, left half-planes depending on the lag and containing all zeros of the characteristic function are obtained. A sufficient lag- independent condition for the whole class considered is found. For the neutral case a collection of disks covering all zeros of the characteristic function is given. A simple example of a neutral characteristic function is given. Zero-free neighbourhoods of the zeros of the coefficient polynomials are devised. A discussion of some special aspects concludes the paper.