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H∞ master-slave synchronization for delayed impulsive implicit hybrid neural networks based on memory-state feedback

Zekun Wang1, Guangming Zhuang1, Xiangpeng Xie2

  • 1School of Mathematical Sciences, Liaocheng University, Liaocheng Shandong 252059, PR China.

Neural Networks : the Official Journal of the International Neural Network Society
|June 23, 2023
PubMed
Summary

This study achieves H∞ master-slave synchronization for delayed impulsive neural networks using memory-state feedback control. The method ensures system stability and performance, even with time-varying delays.

Keywords:
master–slave synchronizationDelayed impulsive neural networksFree-weighting matrix approachImplicit/singular Markov jump systemsMemory-state feedback control

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Area of Science:

  • Control Theory
  • Neural Networks
  • Systems Engineering

Background:

  • Master-slave synchronization is crucial for complex systems.
  • Delayed impulsive hybrid neural networks present significant control challenges.
  • Ensuring H∞ performance under uncertainty is a key requirement.

Purpose of the Study:

  • To investigate the H∞ master-slave synchronization for delayed impulsive implicit hybrid neural networks.
  • To develop a robust memory-state feedback control strategy.
  • To achieve guaranteed performance indices and system admissibility.

Main Methods:

  • Development of a stochastic impulse-time-dependent Lyapunov-Krasovskii functional.
  • Application of memory-state feedback control.
  • Utilizing linear matrix inequalities (LMIs) for controller design.
  • Employing the free-weighting matrix technique to handle time-varying delays.

Main Results:

  • The closed-loop system achieves stochastic admissibility and prescribed H∞ performance.
  • A mode-dependent memory-state feedback synchronization controller is successfully designed.
  • The method effectively relaxes constraints on the derivative of time-varying delays.
  • Simulation results on a genetic regulatory network validate the approach.

Conclusions:

  • The proposed memory-state feedback control effectively solves the H∞ master-slave synchronization problem for the targeted neural networks.
  • The developed Lyapunov-Krasovskii functional and control design techniques offer a generalized framework for similar complex systems.
  • The findings have potential applications in bio-economic systems and other fields requiring synchronized complex dynamics.