# On the Ball-Marsden-Slemrod obstruction for bilinear control systems

## TL;DR

This paper extends a well-known result on the limitations of controlling bilinear systems in infinite-dimensional spaces to include $L^1$-controls, highlighting fundamental obstructions to controllability.

## Contribution

It generalizes the Ball--Marsden--Slemrod obstruction to the case of $L^1$-controls in infinite-dimensional bilinear control systems.

## Key findings

- Obstruction to controllability persists with $L^1$-controls.
- Extension of classical results to broader control spaces.
- Highlights fundamental limitations in infinite-dimensional control systems.

## Abstract

In this paper we present an extension to the case of $L^1$-controls of a famous result by Ball--Marsden--Slemrod on the obstruction to the controllability of bilinear control systems in infinite dimensional spaces.