Laguerre-Based Low-Rank Balanced Truncation of Discrete-Time Systems

Abstract

In this brief, a new model order reduction method based on low-rank Gramian approximation is proposed for discrete-time systems. The main task is to use the Laguerre functions expansions to calculate the approximate low-rank decomposition factors of the controllability and observability Gramians, which are calculated by the recurrence formulas. Then, the reduced-order systems are obtained by the low-rank square root method which approximate the original system well. In addition, due to the disadvantages of the above method that it may produce an unstable system even if the original system is stable, a modified reduction procedure is proposed, which can preserve stability in some cases. It combines the dominant subspace projection method to use the sum of both subspaces for a state space projection. The effectiveness of the proposed methods are illustrated by two numerical examples.