Nonlinear feedback controller for the synchronization of hyper (Chaotic) systems with known parameters

Muhammad Haris*, Muhammad Shafiq, Adyda Ibrahim, Masnita Misiran

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


This paper proposes, designs, and analyses a novel nonlinear feedback controller that realizes fast, and oscillation free convergence of the synchronization error to the equilibrium point. Oscillation free convergence lowers the failure chances of a closed-loop system due to the reduced chattering phenomenon in the actuator motion, which is a consequence of low energy sm ooth control signal. The proposed controller has a novel structure. This controller does not cancel nonlinear terms of the plant in the closed-loop; this attribute improves the robustness of the loop. The controller consists of linear and nonlinear parts; each part executes a specific task. The linear term in the controller keeps the closed-loop stable, while the nonlinear part of the controller facilitates the fast convergence of the error signal to the vicinity of the origin. Then the linear controller synthesizes a smooth control signal that moves the error signals to zero without oscillations. The nonlinear term of the controller does not contribute to this synthesis. The collaborative combination of linear and nonlinear controllers that drive the synchronization errors to zero is innovative. The paper establishes proof of global stability and convergence behavior by describing a detailed analysis based on the Lyapunov stability theory. Computer simulation results of two numerical examples verify the performance of the proposed controller approach. The paper also provides a comparative study with state-of-the-art controllers.

Original languageEnglish
Pages (from-to)124-135
Number of pages12
JournalJournal of Mathematics and Computer Science
Issue number2
Publication statusPublished - 2020


  • Chaotic system
  • Lyapunov stability
  • Nonlinear feedback controller
  • Synchronization

ASJC Scopus subject areas

  • Computational Mechanics
  • Mathematics(all)
  • Computer Science Applications
  • Computational Mathematics


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