On computing the maximal delay intervals for stability of linear delay systems

This note is concerned with stability properties of linear time-invariant delay systems. The authors consider delay systems of both retarded and neutral types expressed in state-space forms. The author´s main goal is to provide a computation-oriented method for computing the maximal delay intervals over which the systems under consideration maintain stability. The author´s results show that this can be accomplished by computing the generalized eigenvalues of certain frequency-dependent matrices. Based on these results, the author also states a necessary and sufficient condition concerning stability independent of delay for each of the retarded and neutral systems. The author´s results can be readily implemented and appear suitable for analyzing systems with high dimensions and many delay units