# The Riesz basis property of a class of Euler-Bernoulli beam equation

## TL;DR

This paper proves that a specific set of eigenvectors for a controlled Euler-Bernoulli beam system forms a Riesz basis, ensuring exponential stability of the system.

## Contribution

It establishes the Riesz basis property for eigenvectors of a beam equation under boundary feedback, which was previously unproven.

## Key findings

- Eigenvectors form a Riesz basis
- Closed-loop system is exponentially stable
- Provides a basis for stability analysis

## Abstract

In this paper, we prove that a sequence of generalized eigenvectors of a linear unbounded operator associated with an Euler-Bernoulli beam equation under bending moment boundary feedback forms a Riesz basis for the underlying state Hilbert space. As a consequence, the resulting closed-loop system is exponentially stable.