Frequency-constrained Gramian-based precision-focused balanced truncation for linear time-invariant discrete-time systems

Model order reduction for discrete-time systems is often required to preserve accuracy over a prescribed frequency interval rather than across the entire frequency range. It is observed that a few existing methods based on frequency-constrained Gramians yield significant approximation errors for discrete-time systems owing to the eigenvalue imbalance in some of the intermediate matrices. Therefore, in this paper, a novel model reduction technique is proposed for discrete-time systems by constructing new frequency-constrained Gramians. A novel set of pseudo-input and output matrices is formed that precisely approximates the higher-order system to a lower-order system within the specified frequency interval. The proposed method guarantees a stable reduced model for a given stable system and provides an a priori error bound for the desired frequency interval. The simulation results of numerical examples illustrate the effectiveness of the proposed technique.