Discrete system reduction via impulse-response Gramians and its relation to q-Markov covers

A method for model reduction of linear discrete systems is proposed. It is based on the impulse-response Gramian proposed by the authors (1989) for discrete systems. This Gramian is an extension of the one proposed for linear continuous systems and contains information on the input-output behavior of the system. The rth-order reduced-order models are made to retain the first r Markov parameters and the first r×r elements of the impulse-response Gramian of the original system. The relation between this method and the q-Markov cover method is also discussed. The method is illustrated by a numerical example