# Balanced Truncation of Linear Systems with Quadratic Outputs in Limited Time and Frequency Intervals

arXiv: https://arxiv.org/abs/2402.11445 · HTML: https://mlsanity.com/paper/2402.11445/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2024.

## Built on by (most cited first, 1 of 1)

- [A Deep State-Space Model Compression Method using Upper Bound on Output Error](https://mlsanity.com/paper/2510.14542/) (2025)

## Abstract (arXiv)

Model order reduction involves constructing a reduced-order approximation of a high-order model while retaining its essential characteristics. This reduced-order model serves as a substitute for the original one in various applications such as simulation, analysis, and design. Often, there's a need to maintain high accuracy within a specific time or frequency interval, while errors beyond this limit can be tolerated. This paper addresses time-limited and frequency-limited model order reduction scenarios for linear systems with quadratic outputs, by generalizing the recently introduced structure-preserving balanced truncation algorithm. To that end, limited interval system Gramians are defined, and the corresponding generalized Lyapunov equations governing their computation are derived. Additionally, low-rank solutions for these equations are investigated. Next, balanced truncation algorithms are proposed for time-limited and frequency-limited scenarios, each utilizing its corresponding limited-interval system Gramians. The proposed algorithms ensure accurate results within specified time and frequency intervals while preserving the quadratic-output structure. Two benchmark numerical examples are presented to demonstrate the effectiveness of the algorithms, showcasing their ability to achieve superior accuracy within the desired time or frequency interval.