2024/02/18 by Qiu‐Yan Song, Song, Qiu-Yan, Umair Zulfiqar +7 · 1 citation
Computer Science · Engineering · #Control Systems and Identification #FOS: Electrical engineering #Mathematical Control Systems and Analysis #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2402.11445
openalex publication_date 2024/02/18 · openalex created_date 2024/02/22 · openalex updated_date 2026/07/28
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.