# Koopman-based feedback design with stability guarantees

arXiv: https://arxiv.org/abs/2312.01441 · HTML: https://mlsanity.com/paper/2312.01441/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2023.

## Built on by (most cited first, 5 of 5)

- [SafEDMD: A Koopman-based data-driven controller design framework for nonlinear dynamical systems](https://mlsanity.com/paper/2402.03145/) (2024)
- [End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic data](https://mlsanity.com/paper/2409.18010/) (2024)
- [Uncertainty Modelling and Robust Observer Synthesis using the Koopman Operator](https://mlsanity.com/paper/2410.01057/) (2024)
- [Koopman operator theory: fundamentals, control, and applications](https://mlsanity.com/paper/2607.01819/) (2026)
- [Data-Driven Predictive Control of Nonholonomic Robots Based on a Bilinear Koopman Realization: Data Does Not Replace Geometry](https://mlsanity.com/paper/2411.07192/) (2024)

## Abstract (arXiv)

We present a method to design a state-feedback controller ensuring exponential stability for nonlinear systems using only measurement data. Our approach relies on Koopman-operator theory and uses robust control to explicitly account for approximation errors due to finitely many data samples. To simplify practical usage across various applications, we provide a tutorial-style exposition of the feedback design and its stability guarantees for single-input systems. Moreover, we extend this controller design to multi-input systems and more flexible nonlinear state-feedback controllers using gain-scheduling techniques to increase the guaranteed region of attraction. As the proposed controller design is framed as a semidefinite program, it allows for an efficient solution. Further, we enhance the geometry of the region of attraction through a heuristic algorithm that establishes a connection between the employed Koopman lifting and the dynamics of the system. Finally, we validate the proposed feedback design procedure by means of numerical examples.