Recently Azou et al. proposed a method of model reduction for discrete systems based on a new impulse response Gramian. The reduced model was derived by first approximating the low-order impulse response Gramian, and then matching some Markov parameters and time-moments of an original model. In this note a modified method is presented so that the reduced model exactly preserves the low-order impulse response Gramian together with a slightly different set of Markov parameters and time-moments of the original model.

We present a minimal lattice realization of MIMO linear discrete-time systems which interpolate the desired Markov and covariance parameters. The minimal lattice realization is derived via a recursive construction algorithm based on the state space description and it parametrizes all the interpolants.