Finite-Time Stability and Stabilization of Impulsive Stochastic Delayed Neural Networks With Rous and Rons

Tao Chen,Yinghan Hong,Shiguo Peng,Guizhen Mai

doi:10.1109/access.2020.2992686

Tao Chen, Yinghan Hong + Show 2 more

Open Access

https://doi.org/10.1109/access.2020.2992686

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Abstract

This paper mainly tends to investigate finite-time stability and stabilization of impulsive stochastic delayed neural networks with randomly occurring uncertainties (ROUs) and randomly occurring nonlinearities (RONs). Firstly, by constructing the proper Lyapunov-Krasovskii functional and employing the average impulsive interval method, several novel criteria for ensuring the finite-time stability of impulsive stochastic delayed neural networks are obtained by means of linear matrix inequalities (LMIs). Then, some conditions about the state feedback controller are derived to ensure the finite-time stabilization of impulsive stochastic delayed neural networks with ROUs and RONs. Finally, numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed results.

Highlights

Neural networks (NNs) are usually considered as one of the simplified models of neural processing in human brain [1]–[5]
This paper considers a class of impulsive stochastic delayed neural networks (ISDNNs) with randomly occurring uncertainties (ROUs) and randomly occurring nonlinearities (RONs), which has just a little research
By structuring proper Lyapunov-Krasovskii functional and by means of the average impulsive interval method, some new finite-time stability criteron in terms of linear matrix inequalities (LMIs) are derived for ISDNNs with ROUs and RONs

Summary

INTRODUCTION

Neural networks (NNs) are usually considered as one of the simplified models of neural processing in human brain [1]–[5]. For the NNs with impulsive effects and time-varing delay, authors in [34] demonstrated the finite-time stability by means of Lyapunov-Krasovskii functional and the average impulsive interval method whether it was the stabilizing impulses or the destabilizing impulses. A great deal of stability or stabilization results of dynamic systems have been obtained in many existing papers [14]–[16], [19], [22]–[25], [35], finite-time stability and stabilization results of impulsive stochastic delayed neural networks (ISDNNs) with ROUs and RONs are still very few. By structuring proper Lyapunov-Krasovskii functional and by means of the average impulsive interval method, some new finite-time stability criteron in terms of LMI are derived for ISDNNs with ROUs and RONs. Let , F , {Ft }t 0 , P be a complete probability space with filtration {Ft }t 0 satisfying the usual conditions (i.e., the filtration contains all P-null sets and is right continuous), and E {·} stands for the mathematical expectation operator with respect to a given probability measure P

PROBLEM STATEMENT AND PRELIMINARIES

NUMERICAL EXAMPLES

CONCLUSION