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This study develops a memory sampled-data controller for complex dynamical systems (CDNs) with input saturation and transmission delays. The method ensures exponential synchronization and estimates the basin of attraction.

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Area of Science:

  • Control Theory
  • Dynamical Systems
  • Nonlinear Control

Background:

  • Complex dynamical systems (CDNs) often exhibit input saturation, limiting control effectiveness.
  • Transmission delays introduce significant challenges in achieving stable synchronization.
  • Existing methods may not adequately address both saturation and delay simultaneously.

Purpose of the Study:

  • To design an exponential synchronization controller for complex dynamical systems (CDNs) with input saturation.
  • To account for the effects of transmission delay using a memory sampled-data approach.
  • To estimate and enlarge the region of attraction for the synchronized system.

Main Methods:

  • A memory sampled-data controller is designed to handle input saturation and transmission delays.
  • A modified two-sided looped functional is constructed, considering current and delayed state information.
  • Sufficient criteria for exponential synchronization are derived using Lyapunov stability theory.

Main Results:

  • The proposed controller guarantees exponential synchronization for CDNs with input saturation and transmission delay.
  • The method provides an estimation of the basin of attraction for the synchronization error.
  • An optimization algorithm is presented to enlarge the region of attraction.

Conclusions:

  • The developed memory sampled-data control strategy effectively achieves exponential synchronization in complex dynamical systems under input saturation and transmission delays.
  • The proposed approach offers a robust method for analyzing and enhancing the stability and performance of such systems.
  • Numerical simulations validate the theoretical findings and demonstrate the controller's practical applicability.