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Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks
IEEE Transactions on Neural Networks and Learning Systems
|March 21, 2015
Summary
This study introduces new methods for stabilizing and synchronizing discrete-time delayed neural networks (DDNNs) using impulses. The findings offer criteria for exponential stability and enable synchronization of chaotic DDNNs for secure communication.
Area of Science:
- Control Theory
- Computational Neuroscience
- Applied Mathematics
Background:
- Discrete-time delayed neural networks (DDNNs) present complex dynamics.
- Impulsive control strategies are crucial for stabilizing and synchronizing such systems.
- Existing methods often struggle with time delays and require specific interval lengths.
Purpose of the Study:
- To investigate impulsive stabilization and synchronization for discrete-time delayed neural networks (DDNNs).
- To develop novel criteria for exponential stability in DDNNs with stabilizing impulses.
- To propose an impulsive synchronization scheme for identical DDNNs, even with unknown delays.
Main Methods:
- Introduction of a time-varying Lyapunov functional to analyze system dynamics.
- Application of a convex combination technique for deriving stability criteria.
- Development of linear-state feedback impulsive controllers.
- Proposal of a novel impulsive synchronization scheme for identical DDNNs.
Main Results:
- New exponential stability criteria derived using linear matrix inequalities.
- Stability criteria are independent of time delay size but dependent on impulsive interval lengths.
- Sufficient conditions for the existence of linear-state feedback impulsive controllers are established.
- A novel impulsive synchronization scheme effectively synchronizes identical DDNNs with unknown delays.
Conclusions:
- The derived criteria provide effective methods for impulsive stabilization and synchronization of DDNNs.
- The proposed synchronization scheme has practical applications, such as in secure communication using chaotic DDNNs.
- Simulation results validate the effectiveness of the presented theoretical findings.
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