A Lyapunov-based novel fixed-time control scheme for chaotic systems synchronization

• Introduced a generalized fixed-time synchronization control (FTSC) law for synchronizing chaotic systems. • It relaxes reliance on Jensen's inequality and the Lipschitz condition for fixed-time stability, reducing theoretical and computational complexity. • It utilizes a single exponential feedback term in the control protocols along with other controller components, ensuring smooth, rapid convergence to the origin. • It effectively mitigates chattering and external disturbances. • It achieves 75% faster synchronization, 68.75% quicker energy dissipation, and 72% lower energy consumption than conventional FTSC methods. Chaos synchronization is a fundamental problem in control theory with broad applications in secure communications, robotics, power systems, and biological networks. Fixed-time synchronization control (FTSC) guarantees convergence within a predefined time, independent of initial conditions. However, many existing FTSC schemes rely on restrictive assumptions, such as Jensen’s inequality and Lipschitz continuity, which increase analytical and computational complexity. Moreover, these control approaches often yield highly oscillatory control inputs, slower convergence, and excessive energy consumption. This paper proposes a novel Lyapunov-based FTSC framework that removes these restrictive assumptions by incorporating a single-power-law feedback term, along with linear and nonlinear components, into the controller design. The single power-law and a signum term are introduced to establish fixed-time stability with reduced computational burden analytically. The hyperbolic feedback term provides smooth convergence and mitigates chattering. The proposed control approach effectively enhances robustness against various bounded time-varying disturbances. As a result, the proposed controller achieves fast convergence, smooth control behavior, and improved energy efficiency. Closed-loop fixed-time stability is rigorously established using Lyapunov theory. Numerical simulations of chaotic permanent-magnet synchronous motor systems in a master-slave configuration demonstrate the effectiveness of the proposed approach. Comparative results show that the proposed FTSC scheme achieves 75% faster synchronization, 69% lower energy consumption, and a 72% improvement in the energy dissipation rate compared with state-of-the-art FTSC methods. These findings confirm that the proposed strategy provides a computationally efficient, energy-efficient, and robust solution for chaos synchronization, advancing both theoretical development and practical implementation of fixed-time control techniques in nonlinear systems.