On computing the zeros of periodic systems

We present an efficient and numerically reliable approach to compute the zeros of a periodic system. The zeros are defined in terms of the transfer-function matrix corresponding to an equivalent lifted statespace representation as constant system. The proposed method performs locally row compressions of the associated system pencil to extract a low order pencil which contains the zeros (both finite and infinite) as well as the Kronecker structure of the periodic system. The proposed algorithm belongs to the family of fast, structure exploiting algorithms and relies exclusively on using orthogonal transformations. For the overall zeros computation a certain form of numerical stability can be ensured.