# An Input-Output Parametrization of Stabilizing Controllers: amidst Youla and System Level Synthesis

arXiv: https://arxiv.org/abs/1903.03828 · HTML: https://mlsanity.com/paper/1903.03828/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2019.

## Built on by (most cited first, 3 of 3)

- [Learning to Boost the Performance of Stable Nonlinear Systems](https://mlsanity.com/paper/2405.00871/) (2024)
- [Stabilizing reinforcement learning control: A modular framework for optimizing over all stable behavior](https://mlsanity.com/paper/2310.14098/) (2023)
- [Combining Federated Learning and Control: A Survey](https://mlsanity.com/paper/2407.11069/) (2024)

## Abstract (arXiv)

This paper proposes a novel input-output parametrization of the set of internally stabilizing output-feedback controllers for linear time-invariant (LTI) systems. Our underlying idea is to directly treat the closed-loop transfer matrices from disturbances to input and output signals as design parameters and exploit their affine relationships. This input-output perspective is particularly effective when a doubly-coprime factorization is difficult to compute, or an initial stabilizing controller is challenging to find; most previous work requires one of these pre-computation steps. Instead, our approach can bypass such pre-computations, in the sense that a stabilizing controller is computed by directly solving a linear program (LP). Furthermore, we show that the proposed input-output parametrization allows for computing norm-optimal controllers subject to quadratically invariant (QI) constraints using convex programming.