Flows of vector fields and the Kalman Theorem
Optimization and Control
2025-03-07 v2 Differential Geometry
Abstract
We give two proofs of the Kalman Theorem, alternative to the most common ones, which infer such a classical result of Control Theory using just very basic facts on flows of vector fields. These proofs are apt to be generalised in diverse directions -- in fact one of them has been already generalised, yielding new criteria for local controllability of non-linear real analytic controlled systems.
Cite
@article{arxiv.2412.07438,
title = {Flows of vector fields and the Kalman Theorem},
author = {Fabio Bagagiolo and Cristina Giannotti and Andrea Spiro and Marta Zoppello},
journal= {arXiv preprint arXiv:2412.07438},
year = {2025}
}