On backward shift algorithm for estimating poles of systems

In this paper, we present an algorithm for estimating poles of linear time-invariant systems by using the backward shift operator. We prove that poles of rational functions, including zeros and multiplicities, are solutions to an algebraic equation which can be obtained by taking backward shift operator to the shifted Cauchy kernels in the unit disc case. The algorithm is accordingly developed for frequency-domain identification. We also prove the robustness of this algorithm. Some illustrative examples are presented to show the efficiency in systems with distinguished and multiple poles.