# H2-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation

arXiv: https://arxiv.org/abs/2505.03057 · HTML: https://mlsanity.com/paper/2505.03057/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2025.

## 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)

This paper addresses the H2-optimal approximation of linear dynamical systems with quadratic-output functions, also known as linear quadratic-output systems. Our major contributions are threefold. First, we derive interpolatory first-order optimality conditions for the linear quadratic-output H2 minimization problem. These conditions correspond to the mixed-multipoint tangential interpolation of the full-order linear- and quadratic-output transfer functions, and generalize the Meier-Luenberger optimality framework for the H2-optimal model reduction of linear time-invariant systems. Second, given the optimal interpolation data, we show how to enforce the interpolatory optimality conditions explicitly by Petrov-Galerkin projection of the full-order model. Third, to find the optimal interpolation data, we build on this projection framework and propose a generalization of the iterative rational Krylov algorithm for the H2-optimal model reduction of linear quadratic-output systems, called LQO-IRKA. Upon convergence, LQO-IRKA produces reduced linear quadratic-output systems that satisfy the interpolatory optimality conditions. The method only requires solving shifted linear systems and matrix-vector products, thus making it suitable for large-scale problems. Numerical examples are included to illustrate the effectiveness of the proposed method.