# Feedback stabilization for a bilinear control system under weak observability inequalities

## TL;DR

This paper develops a feedback stabilization method for bilinear control systems with weak observability, providing explicit decay rates and applications to Schrödinger and wave equations.

## Contribution

It introduces a novel stabilization approach under weak observability conditions and derives explicit decay rates for regular initial data.

## Key findings

- Explicit weak decay rates for bilinear systems
- Application to Schrödinger and wave equations
- Stability analysis under weak observability

## Abstract

In this paper, we discuss the feedback stabilization of bilinear systems under weak observation properties. In this case, the uniform stability is not guaranteed. Thus we provide an explicit weak decay rate for all regular initial data. Applications to Schr\"odinger and wave equations are provided.