Reliable algorithms for computing minimal dynamic covers

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 rational equations. We propose numerically reliable algorithms to compute two basic types of minimal dimension dynamic covers for a linear system. The proposed approach is based on a special controllability staircase condensed form of a structured pair (A, [B₁, B₂]), which can be computed using exclusively orthogonal similarity transformations. Using such a condensed form minimal dimension covers and corresponding feedback/feedforward matrices can be easily computed. The overall algorithm has a low computational complexity and is provably numerically reliable.