Computing the zeros of periodic descriptor systems

Abstract

In this paper, we give a numerically reliable algorithm to compute the zeros of a periodic descriptor system. The algorithm is a variant of the staircase algorithm applied to the system pencil of an equivalent lifted time-invariant state-space system and extracts a low-order pencil which contains the zeros (both finite and infinite) as well as the Kronecker structure of the periodic descriptor system. The proposed algorithm is efficient in terms of complexity by exploiting the structure of the pencil and is exclusively based on orthogonal transformations, which ensures some form of numerical stability.