Finite-time stability for differential inclusions with applications to neural networks

TL;DR

This paper establishes conditions for finite-time stability of differential inclusions using Lyapunov functions and Gronwall-type estimates, with applications demonstrated on neural networks.

Contribution

It introduces new criteria for finite-time stability of differential inclusions and applies these results to neural network models.

Findings

Derived sufficient conditions for finite-time stability.

Developed new Gronwall-type estimates for settling time.

Provided an example of a neural network exhibiting finite-time stability.

Abstract

The paper investigates sufficient conditions on a differential inclusion which guarantee that the origin is a finite time stable equilibrium, namely a weak local one, a weak global one or a strong local one. The analysis relies on the existence of a Lyapunov function. A new Gronwall type results are used to estimate the settling time. An example of a neural network which is finite-time stable is given