$\mathcal{H}_\infty$ model order reduction for quadratic output systems
Optimization and Control
2025-05-20 v1 Dynamical Systems
Abstract
Linear time-invariant quadratic output (LTIQO) systems generalize linear time-invariant systems to nonlinear regimes. Problems of this class occur in multiple applications naturally, such as port-Hamiltonian systems, optimal control, and stochastical problems. We introduce an -norm for LTIQO systems with one or multiple outputs and propose an algorithm to optimize a reduced order model (ROM) to be close in the -norm to a given full order model. We illustrate the applicability and the performance with an established numerical example and compare the resulting ROMs with results from balanced truncation and -focussed algorithms.
Keywords
Cite
@article{arxiv.2505.12529,
title = {$\mathcal{H}_\infty$ model order reduction for quadratic output systems},
author = {Birgit Hillebrecht and Benjamin Unger},
journal= {arXiv preprint arXiv:2505.12529},
year = {2025}
}