Dynamical analysis and robust control of a memristor-based four-dimensional chaotic system: <i>H</i> _∞ control and active–anti-control methods

Abstract This study develops a four-dimensional memristor-based chaotic system and undertakes a comprehensive investigation of its dynamics and robust control. For control, an H ∞ state-feedback scheme is designed and shown to maintain stable system output under external disturbances, offering a new avenue for memristive chaos regulation. To further explore manipulation of chaotic behaviour, two complementary strategies are examined: active control, which suppresses chaos and stabilises the state at an equilibrium point, and anti-control, which dynamically amplifies the nonlinear coupling to intensify chaos. Both approaches are validated through combined circuit and numerical experiments. Classical analytical tools reveal that the system possesses a rich set of nonlinear characteristics. Hardware feasibility is verified via circuit simulation: a detailed Multisim model is built and the resulting attractors are captured on an oscilloscope, closely matching numerical predictions. The proposed system therefore provides a promising platform for secure communication, random-number generation and other nonlinear-dynamics-based technologies, while the dual (suppression/enhancement) control framework supplies fresh theoretical insight and practical guidance for the control and synchronisation of high-dimensional chaotic systems.