# Limitations of LTI Koopman Modeling for Nonlinear Control Systems

arXiv: https://arxiv.org/abs/2604.25290 · HTML: https://mlsanity.com/paper/2604.25290/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Apr 2026.

## Built on by (most cited first, 2 of 2)

- [Koopman operator theory: fundamentals, control, and applications](https://mlsanity.com/paper/2607.01819/) (2026)
- [Learning to control switching nonlinear systems with Koopman operator regression](https://mlsanity.com/paper/2607.11344/) (2026)

## Abstract (arXiv)

Koopman operator theory yields powerful tools for modeling, analysis, and control of nonlinear dynamical systems. Prominently, linear time-invariant (LTI) Koopman representations have been proposed to enable the application of linear control techniques, such as LQR and convex MPC. In this work, we investigate the implications of exact LTI Koopman representations for continuous-time nonlinear control systems. In particular, we show that, assuming a mild controllability condition and the inclusion of the coordinate maps, the dynamics of the underlying control system must be affine linear. Furthermore, we study the modeling bias introduced by the LTI structure and analyze its dependency on the choice of observables.