Discrete systems reduction via impulse-response Grammians and its relation to q-Markov covers

A new method for model reduction of linear discrete systems is proposed. It is based on the impulse-response Grammian proposed for discrete systems. This Grammian 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 Grammian of the original system. The relation between this method and the q-Markov cover method is discussed.<>