# New Results on Finite-Time Stability: Geometric Conditions and Finite-Time Controllers

## TL;DR

This paper introduces new geometric conditions and controllers that ensure finite-time stability for linear systems, with theoretical proofs and simulation results demonstrating their effectiveness.

## Contribution

It provides novel geometric conditions for finite-time stability and develops new controllers based on vector fields and barrier functions for linear systems.

## Key findings

- Finite-time stability condition for scalar systems
- Novel controllers based on vector fields and barrier functions
- Simulation results confirm controller efficacy

## Abstract

This paper presents novel controllers that yield finite-time stability for linear systems. We first present a sufficient condition for the origin of a scalar system to be finite-time stable. Then we present novel finite-time controllers based on vector fields and barrier functions to demonstrate the utility of this geometric condition. We also consider the general class of linear controllable systems, and present a continuous feedback control law to stabilize the system in finite time. Finally, we present simulation results for each of these cases, showing the efficacy of the designed control laws.