Global Mittag-Leffler stability of Fractional-Order Projection Neural Networks with Impulses

TL;DR

This paper introduces a new class of fractional-order projection neural networks with impulses, establishing their solution existence, stability, and providing numerical examples to validate the theoretical results.

Contribution

It develops a framework for fractional-order impulsive neural networks, proving solution existence, boundedness, and global Mittag-Leffler stability with Lyapunov methods.

Findings

Solutions exist and are bounded under mild conditions.

Global Mittag-Leffler stability is achieved for the equilibrium point.

Numerical examples confirm theoretical results.

Abstract

This paper is about the study of a new class of fractional-order projection neural networks with impulses which capture the desired features of both the variational inequality and the fractional-order impulsive dynamical systems within the same framework. We obtain the existence and boundedness of solutions for such fractional-order projection neural networks under mild conditions. Moreover, we give some sufficient conditions for ensuring the global Mittag-Leffler stability of the equilibrium point for such fractional-order projection neural networks by utilizing a general quadratic Lyapunov function. Finally, we provide two numerical examples to illustrate the validity and feasibility of the main results.