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. The class of all such systems is parameterized. 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