On the zeros of quasi-polynomials with single delay

A new numerical method is introduced for calculation of quasi-polynomial zeros with constant single delay. The trajectories of zeros are obtained depending on time-delay from zero to final time-delay value. The method determines all the zeros of the quasi-polynomial in any right half-plane. The approach is used to determine stability analysis of time-delay systems. The method is easy to implement, robust and applicable to quasi-polynomials with high order. The effectiveness of the method is shown on an example.