A spectral element approach for the stability analysis of time-periodic delay equations with multiple delays

This paper describes a general spectral element approach to study the stability of multiple time delay systems (MTDS). We show, for the first time, how this approach can be applied to periodic MTDS where the delays and the period are incommensurate. In contrast to prior works on MTDS, the spectral element approach is applicable to both autonomous as well as non-autonomous MTDS. Both MTDS of first order or higher can be obtained and systems with or without damping can be investigated. Since the spectral element approach uses efficient interpolation and a set of well-distributed interpolation points, the size of the matrices necessary for convergence is kept small. Further, since the spectral element approach is a semi-analytical procedure, it avoids the need to use tedious time marching algorithms to explore the stability behavior of the system.

► We present an approach to study periodic multiple time delay systems (MTDS).
► This approach can study the stability of general periodic delay equations.
► It can also find the stability of MTDS with incommensurate delays.
► The presented approach uses smaller matrices than extant methods.
► Handling incommensurate delays also makes it relatively more robust.