A piecewise LKF-based method for non-weighted L2-gain H∞ global asymptotic synchronization of switched nonlinear time-delay systems

This paper investigates the problem of non-weighted L2-gain H∞ global asymptotic synchronization (GAS) for switched nonlinear master–slave systems subject to time-varying delays and external disturbances. A mode-dependent piecewise Lyapunov–Krasovskii functional (LKF) method is proposed. We divide the dwell-time (DT) interval of each mode into two segments. At each partition point, we introduce a mode-dependent Lyapunov coefficient μr greater than 1. This strategy, combined with the average dwell-time (ADT) condition and compensation via the exponential decay rate α, significantly improves the design flexibility of the system controller. Furthermore, it strictly restricts the jump magnitudes of the LKF at both subinterval switching points and mode switching points. Consequently, the conservatism of traditional methods is markedly reduced. Simultaneously, the proposed approach still achieves GAS and robustness under frequent switching. Theoretical analysis shows that the proposed method strictly guarantees the global asymptotic convergence of the synchronization error and achieves disturbance attenuation under a non-weighted L2-gain. Numerical simulation results serve to confirm both the effectiveness and feasibility of the method put forward in this study, offering a new perspective for synchronization control in complex switched systems.