MAPPING THE SPECTRUM OF A RETARDED TIME-DELAY SYSTEM UTILIZING ROOT DISTRIBUTION FEATURES

An original method for computing the spectrum of a retarded time delay system over a large region in the complex plane is presented. The method is based on mapping the quasi-polynomial characteristic function and on utilizing asymptotic properties of the root chains. First, asymptotic exponentials of the root chains are assessed and large areas free of the roots are determined. These areas are then omitted in systematic mapping of the roots location. The roots are located as the intersection points of the contours determined by real and imaginary parts of the characteristic function. The theoretical explanation of the method is supplemented with a discussion of implementation issues and an application example is added.