ANALYSIS OF INFINITE SPECTRA OF TIME DELAY SYSTEMS USING QUASIPOLYNOMIAL ROOT FINDER IMPLEMENTED IN MATLAB

Abstract: Two original algorithms for computing the roots of low order quasipolynomials are introduced in the paper. The first algorithm is based on Weyl's construction combined with argument principle rule. The second algorithm is based on quasipolynomial function mapping in the complex plane. Both algorithms provide the approximate positions of the roots located inside a selected region. The accuracy of the roots is then increased by using Newton's iteration method. The quasipolynomial rootfinder using the second algorithm has been implemented in Matlab. The presented algorithms provide the significant contribution to the analysis of time delay systems, whose characteristic functions are of the quasipolynomial form