# The Hautus test for non-autonomous linear evolution equation

## TL;DR

This paper extends the Hautus test to non-autonomous linear evolution equations with time-dependent operators, providing a new criterion for controllability in such systems.

## Contribution

It introduces a novel Hautus test applicable to evolution equations with time-dependent operators, advancing controllability analysis for non-autonomous systems.

## Key findings

- Established a Hautus test criterion for non-autonomous systems
- Provided conditions under which the test guarantees controllability
- Extended classical results to time-dependent operator frameworks

## Abstract

In this paper, we investigate the Hautus test for evolution equation with the operators depending on time.