On computing minimal realizations of periodic descriptor systems
We propose computationally efficient and numerically reliable algorithms to compute minimal realizations of periodic descriptor systems. The main computational tool employed for the structural analysis of periodic descriptor systems (i.e., reachability and observability) is the orthogonal reduction of periodic matrix pairs to Kronecker-like forms. Specializations of a general reduction algorithm are employed for particular type of systems. One of the proposed minimal realization methods relies exclusively on structure preserving manipulations via orthogonal transformations for which the backward numerical stability can be proved.