Global Exponential Stability of Fractional Order Complex-Valued Neural Networks with Leakage Delay and Mixed Time Varying Delays

M Hymavathi,Nallappan Gunasekaran,G Muhiuddin,Jehad F Al-Amri,M Syed Ali,R Vadivel

doi:10.3390/fractalfract6030140

Abstract

This paper investigates the global exponential stability of fractional order complex-valued neural networks with leakage delay and mixed time varying delays. By constructing a proper Lyapunov-functional we established sufficient conditions to ensure global exponential stability of the fractional order complex-valued neural networks. The stability conditions are established in terms of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the obtained results.

Highlights

In the past decades, fractional order systems have become an important and hot research field
Around 300 years back, the foundation of fractional order calculus [1–11], which is an extension of classical integer order calculus, was first discussed by Leibniz and L’Hospital, and its development was very slow for a long period
The stability analysis methods for integer order systems such as Lyapunov functional method cannot be generalized to fractional order systems

Summary

Introduction

Fractional order systems have become an important and hot research field. For Instance in [22,23], authors dealt with the existence, uniqueness and global stability of equilibrium point of fractional-order complex valued neural networks with time delays while in [24,25], the synchronization of neural network is investigated. Motivated by the above discussions, in the present endeavor, we have focused on the stability of fractional order complex valued neural networks with leakage and mixed time-varying delays. By making use of a delay differential inequality, we present a new sufficient condition which guarantees global exponential stability of the unique equilibrium point of complex valued neural networks with time-varying delays. (iii) By using Lyapunov functional we obtain the sufficient conditions for global exponential stability neural networks with delays, in terms of LMI, which can be calculated by MATLAB LMI control toolbox. (iv) Numerical examples are given to illustrate the effectiveness of the derived methods

Preliminaries

Mian Results

Numerical Examples

Conclusions