# Thomas Decomposition and Nonlinear Control Systems

arXiv: https://arxiv.org/abs/2001.08424 · HTML: https://mlsanity.com/paper/2001.08424/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2020.

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

- [On boundary conditions parametrized by analytic functions](https://mlsanity.com/paper/2205.03185/) (2022)
- [Physics-informed Gaussian Processes as Linear Model Predictive Controller](https://mlsanity.com/paper/2412.04502/) (2024)

## Abstract (arXiv)

This paper applies the Thomas decomposition technique to nonlinear control systems, in particular to the study of the dependence of the system behavior on parameters. Thomas' algorithm is a symbolic method which splits a given system of nonlinear partial differential equations into a finite family of so-called simple systems which are formally integrable and define a partition of the solution set of the original differential system. Different simple systems of a Thomas decomposition describe different structural behavior of the control system in general. The paper gives an introduction to the Thomas decomposition method and shows how notions such as invertibility, observability and flat outputs can be studied. A Maple implementation of Thomas' algorithm is used to illustrate the techniques on explicit examples.