Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks | JoVE Visualize

Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks

IEEE Transactions on Neural Networks and Learning Systems|March 21, 2015

View abstract on PubMed

Summary

This study presents new methods for stabilizing and synchronizing discrete-time delayed neural networks (DDNNs) using impulses. The findings offer criteria for impulsive stabilization and synchronization, applicable to chaotic systems for secure communication.

Area of Science:

Control Theory
Computational Neuroscience
Network Dynamics

Background:

Discrete-time delayed neural networks (DDNNs) present complex dynamics.
Impulsive control strategies are crucial for stabilizing and synchronizing these networks.
Existing methods often struggle with time delays and network complexity.

Purpose of the Study:

To investigate impulsive stabilization and synchronization of DDNNs.
To develop novel criteria for exponential stability in discrete-time impulsive delayed neural networks (DIDNNs).
To propose an impulsive synchronization scheme for identical DDNNs, even with unknown delays.

Main Methods:

Introduction of a time-varying Lyapunov functional to analyze DIDNN dynamics.
Application of a convex combination technique.
Derivation of stability criteria using linear matrix inequalities (LMIs).

Main Results:

New exponential stability criteria for DIDNNs derived, independent of time delay size but dependent on impulsive interval lengths.
Sufficient conditions for the existence of linear-state feedback impulsive controllers established.
A novel impulsive synchronization scheme for identical DDNNs, including those with unknown delays, demonstrated.

Conclusions:

The proposed criteria effectively address impulsive stabilization and synchronization challenges in DDNNs.
The developed synchronization scheme shows promise for applications like secure communication using chaotic DDNNs.
Simulation results validate the theoretical findings and the practical applicability of the methods.