A new method for computing delay margins for stability of linear delay systems

This note is concerned with stability properties of linear time-invariant delay systems. We consider retarded delay systems modeled both as a high order scalar differential difference equation and as a set of first order differential-difference equations expressed in state space form. We provide a computational method that can be used to compute a delay interval such that the delay system under consideration is stable for all delay values that lie in the computed interval. This method requires computing only the eigenvalues and generalized eigenvalues of certain constant matrices and it can be implemented efficiently. Based on this method, we further state a simple necessary and sufficient condition concerning stability independent of delay for each of the two types of the models