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Delay-range-dependent chaos synchronization approach under varying time-lags and delayed nonlinear coupling.

Muhammad Hamad Zaheer1, Muhammad Rehan1, Ghulam Mustafa1

  • 1Department of Electrical Engineering, Pakistan Institute of Engineering and Applied Sciences (PIEAS), P. O. Box 45650, Islamabad, Pakistan.

ISA Transactions
|December 3, 2014
PubMed
Summary

This study introduces a novel control method for chaos synchronization in nonlinear time-delay systems. The approach ensures reliable synchronization despite time-varying delays and perturbations, enhancing system stability.

Keywords:
Chaos synchronizationDelay-range-dependencyLyapunov–Krasovskii functionalNonlinear time-delay couplingState feedback controlTime-varying delays

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Area of Science:

  • Nonlinear Dynamics and Control Systems
  • Chaos Theory and Synchronization
  • Time-Delay Systems Analysis

Background:

  • Chaos synchronization in coupled nonlinear systems is crucial for secure communication and complex system modeling.
  • Existing methods often struggle with time-varying delays and nonlinear coupling, limiting practical applications.
  • Time-delay systems present unique challenges due to inherent lags in system dynamics and coupling.

Purpose of the Study:

  • To develop a novel delay-range-dependent state feedback control strategy for achieving chaos synchronization.
  • To address the complexities introduced by nonlinear coupling and time-varying intrinsic and coupling delays.
  • To ensure robust synchronization against external perturbations in time-delay chaotic networks.

Main Methods:

  • Utilizing Lyapunov-Krasovskii (LK) functionals to derive delay-range-dependent conditions.
  • Employing linear matrix inequality (LMI) tools for controller synthesis.
  • Formulating a robust state feedback control methodology to minimize L2 gain from disturbance to synchronization error.

Main Results:

  • Established delay-range-dependent conditions for chaos synchronization, considering non-zero lower bounds for delays.
  • Derived a delay-dependent synchronization condition as a special case of the LK functional treatment.
  • Provided a delay-range-dependent condition independent of delay-rate for unknown delay-derivative bounds.
  • Demonstrated the effectiveness of the proposed methodologies through numerical simulations on time-delay chaotic networks.

Conclusions:

  • The proposed delay-range-dependent control approach effectively achieves chaos synchronization in coupled nonlinear time-delay systems.
  • The methodology offers enhanced robustness against perturbations and handles time-varying delays, including unknown delay-rates.
  • The LMI-based approach provides a systematic way to design synchronization controllers for complex time-delay chaotic systems.