Computation of minimal order dynamic covers for periodic systems

Minimal dimension dynamic covers play an important role in solving the structural synthesis problems of minimum order functional observers or fault detectors, or in computing minimal order inverses or minimal degree solutions of model matching problems. We propose numerically reliable algorithms to compute two basic types of minimal dimension dynamic covers for a linear periodic system. The proposed approach is based on a special reachability staircase condensed form, which can be computed using exclusively periodic orthogonal similarity transformations. Using such a condensed form minimal dimension periodic covers and corresponding periodic feedback/feedforward matrices can be easily computed. The overall algorithm has a satisfactory computational complexity and is provably numerically reliable.