The Generation of all q-Markov Covers

Recently developed model reduction procedures lead (for the single input-output case) to qth degree systems with first q-Markov parameters and first q covariance parameters (Markov parameters of the causal part of the power spectrum) taking prescribed values. We parameterize the class of all such systems. For continuous-time systems the class includes an infinite set, whereas for discrete-time the class has only two members. The result is important in that it illustrates the freedom available in a model reduction procedure.