Strongly stable algorithm for computing periodic system zeros

We propose a computationally efficient and numerically reliable algorithm to compute the finite zeros of a linear discrete-time periodic system. The zeros are defined in terms of the transfer-function matrix corresponding to an equivalent lifted time-invariant state-space system. The proposed method relies on structure preserving manipulations of the associated system pencil to extract successively lower complexity subpencils, which contains the finite zeros of the periodic system. The new algorithm uses exclusively structure preserving orthogonal transformations and for the overall computation of zeros the strong numerical stability can be proved.