# Frequency-Domain Identification of Discrete-Time Systems using Sum-of-Rational Optimization

arXiv: https://arxiv.org/abs/2312.15722 · HTML: https://mlsanity.com/paper/2312.15722/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Dec 2023.

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

- [Frequency Response Identification of Low-Order Systems: Finite-Sample Analysis](https://mlsanity.com/paper/2508.17142/) (2025)

## Abstract (arXiv)

We propose a computationally tractable method for the identification of stable canonical discrete-time rational transfer function models, using frequency domain data. The problem is formulated as a global non-convex optimization problem whose objective function is the sum of weighted squared residuals at each observed frequency datapoint. Stability is enforced using a polynomial matrix inequality constraint. The problem is solved globally by a moment-sum-of-squares hierarchy of semidefinite programs through a framework for sum-of-rational-functions optimization. Convergence of the moment-sum-of-squares program is guaranteed as the bound on the degree of the sum-of-squares polynomials approaches infinity. The performance of the proposed method is demonstrated using numerical simulation examples.