Stability of time delay systems using numerical computation of argument principles

The paper proposes a new numerical method to check the stability of a general class of time delay systems. The proposed method checks whether there are characteristic roots whose real values are nonnegative through two steps. First, rectangular bounds of characteristic roots, whose real values are nonnegative, are computed. Next, existence of roots inside the bounds are checked using numerical computation of argument principles. An adaptive discretization is proposed for the numerical computation of argument principles