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Mapping Based Algorithm for Large-Scale Computation of Quasi-Polynomial Zeros

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2 Author(s)
Vyhlidal, T. ; Dept. of Instrum. & Control Eng., Czech Tech. Univ. in Prague, Praha ; Zitek, P.

A method for computing all zeros of a retarded quasi-polynomial that are located in a large region of the complex plane is presented. The method is based on mapping the quasi-polynomial and on utilizing asymptotic properties of the chains of zeros. First, the asymptotic exponentials of the chains are determined based on the distribution diagram of the quasi-polynomial. Secondly, large regions free of zeros are defined. Finally, the zeros are located as the intersection points of the zero-level curves of the real and imaginary parts of the quasi-polynomial, which are evaluated over the areas of the region outside those free of zeros.

Published in:

Automatic Control, IEEE Transactions on  (Volume:54 ,  Issue: 1 )