Computation of Generalized Inverses of Periodic Systems

Abstract

We address the numerically reliable computation of generalized inverses of periodic systems. The underlying inverses are defined via the corresponding lifted repesentations. Structure preserving reduction of the associated system pencil to a special Kronecker-like form is the main computational ingredient for the proposed approach. This form can be computed by employing exclusively orthogonal transformations. For the computational algorithm of the generalized inverse, the backward numerical stability can be proved.