Dynamical analysis and robust control of a memristor‑based four‑dimensional chaotic system: H∞ control and active–anti‑control methods

In this paper, a four‑dimensional memristive chaotic system is proposed and it’s the dynamical evolution as well as robust control strategies are systematically explored. A comprehensive suite of analysis tools—including equilibrium analysis, Lyapunov‑exponent spectra, bifurcation diagrams, coexisting attractors, and Poincaré sections—reveals that the system possesses highly intricate and diverse nonlinear characteristics. To suppress undesired chaos under both parametric uncertainty and external disturbances, an H∞‑based robust controller is devised; numerical simulations confirm that the controller markedly attenuates state amplitudes and enhances disturbance rejection. To broaden the avenues for chaos manipulation, active‑control and anti‑control schemes are comparatively investigated: the former stabilizes trajectories at equilibrium points, whereas the latter amplifies nonlinear coupling to elicit stronger chaos. Consistent results from analog‑circuit emulation and digital simulations verify the feasibility and effectiveness of all proposed methods. Owing to its rich dynamics and controllability, the system is a promising candidate for applications such as secure communication, random‑number generation, and other nonlinear‑dynamics‑based technologies, while also providing fresh theoretical insight and engineering pathways for the control and synchronization of high‑dimensional chaotic systems.