Stability of linear time-delay systems: a delay-dependent criterion with a tight conservatism bound

The stability of linear time-delay systems is investigated via the robustness analysis of a related delay-free comparison system with an uncertain real parameter. By exploiting its phase properties, the delay element is removed from the system via a parameter-dependent Pade approximation. We then present a simple yet rigorous condition for delay-dependent stability of the original time-delay system. The novelty of this result is that it explicitly provides an a priori upper bound of how conservative this condition can be, and this bound depends only on the order of Pade approximation and can be reduced to any desired degree. Furthermore, the delay margin provided by this condition can be computed explicitly without incurring any additional conservatism for the single delay case. This condition can also be checked with some (typically small) additional conservatism by reducing it to finite-dimensional linear matrix inequalities (LMIs). Finally, several numerical examples demonstrate that this simplified LMI criterion can be significantly less conservative than those in the literature.