Balanced Truncation of Linear Systems with Quadratic Outputs in Limited Time and Frequency Intervals
<|reference_start|>Balanced Truncation of Linear Systems with Quadratic Outputs in Limited Time and Frequency Intervals: 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.<|reference_end|>
@article{song2024balanced,
    title={Balanced Truncation of Linear Systems with Quadratic Outputs in Limited
  Time and Frequency Intervals},
    author={Qiu-Yan Song, Umair Zulfiqar, Zhi-Hua Xiao, Mohammad Monir Uddin, and
  Victor Sreeram},
    journal={arXiv preprint arXiv:2402.11445},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.11445},
    primaryClass={eess.SY cs.SY}
}