Numerical computation and new output bounds for time-limited balanced truncation of discrete-time systems

TL;DR

This paper develops new error bounds and efficient numerical methods for time-limited balanced truncation in large-scale discrete-time systems, improving model reduction accuracy within finite time intervals.

Contribution

It introduces novel error bounds for output approximation and proposes strategies for efficient numerical implementation of time-limited balanced truncation.

Findings

Error bounds accurately predict output approximation within time limits

Proposed methods enhance computational efficiency for large-scale systems

Numerical experiments demonstrate improved performance of the techniques

Abstract

In this paper, balancing based model order reduction (MOR) for large-scale linear discrete-time time-invariant systems in prescribed finite time intervals is studied. The first main topic is the development of error bounds regarding the approximated output vector within the time limits. The influence of different components in the established bounds will be highlighted. After that, the second part of the article proposes strategies that enable an efficient numerical execution of time-limited balanced truncation for large-scale systems. Numerical experiments illustrate the performance of the proposed techniques.