Snapshot-based Balanced Truncation for Linear Time-periodic Systems

TL;DR

This paper presents a snapshot-based algorithm for approximate balanced truncation tailored to discrete-time, stable, linear time-periodic systems, capable of handling very high-dimensional systems efficiently.

Contribution

The paper introduces a novel snapshot-based method for balanced truncation applicable to high-dimensional linear time-periodic systems, expanding computational feasibility.

Findings

Validates the method with a practical example

Efficiently handles high-dimensional systems

Applicable to systems with high-dimensional inputs or outputs

Abstract

We introduce an algorithm based on a method of snapshots for computing approximate balanced truncations for discrete-time, stable, linear time-periodic systems. By construction, this algorithm is applicable to very high-dimensional systems, even with very high-dimensional outputs (or, alternatively, very high-dimensional inputs). An example is shown to validate the method.