Generalized dynamic covers for linear systems with applications to deterministic identification and realization problems

Several deterministic identification problems, with partial realization being a special case, are unified in the framework of the mathematical problem "generalized dynamic covers." An algorithm to find such a minimal dynamic cover as well as a uniqueness criterion is given, which yields several identifiability results. This problem also includes the "observer" and the "exact model matching" problems, as well as the problem of finding "minimal inverses for linear systems with arbitrary initial states." It is shown that the problem of finding minimal realizations from a transfer function matrix can also be solved in this framework.