# Finite-time boundary stabilization of general linear hyperbolic balance laws via Fredholm backstepping transformation $\star$

## TL;DR

This paper presents a novel, straightforward proof for the optimal finite control time in linear coupled hyperbolic systems, employing boundary feedback and Fredholm backstepping transformations.

## Contribution

It introduces a new, simple proof method for finite-time stabilization using boundary feedback and Fredholm transformations, enhancing existing control strategies.

## Key findings

- Proof of optimal finite control time
- Design of boundary feedback control law
- Use of Fredholm backstepping transformation

## Abstract

This paper is devoted to a simple and new proof on the optimal finite control time for general linear coupled hyperbolic system by using boundary feedback on one side. The feedback control law is designed by first using a Volterra transformation of the second kind and then using an invertible Fredholm transformation. Both existence and invertibility of the transformations are easily obtained.