Fixed-Time Synchronization of Networked Neutral-Type Filippov Systems with Application to RLC Transmission Line Models

The interconnected RLC circuits are essential nonlinear models for analyzing dynamic coupling and energy transfer in complex electrical networks, serving as a standard testbed for nonsmooth control, time-delay analysis, and synchronization theory research. However, the existing theoretical studies exhibit prominent limitations: most works ignore the dimensional heterogeneity between drive Cresponse circuit subsystems and fail to integrate neutral time delays and Filippov nonsmooth characteristics in system modeling. Moreover, the coordination mechanism between dynamic event-triggered control and indefinite-function-based stability analysis remains underexplored, and incomplete Lyapunov derivative definiteness verification restricts the accuracy and generality of the existing synchronization criteria. Addressing these theoretical gaps, this article investigates the fixed-time (FxT) synchronization control of networked neutral Filippov systems with heterogeneous dimensions. A comprehensive system model is constructed to accommodate dimensional mismatch, neutral time delay, nonsmooth Filippov dynamics, and event-triggered control coupling. Specifically, a novel FxT stability lemma for indefinite functions is proposed to compensate for the defects of conventional Lyapunov analysis methods. Combined with nonsmooth analysis and state-space reconstruction, a rigorous synchronization error model is established for dimension-mismatched systems. Meanwhile, the static and dynamic event-triggered control strategies are designed to reduce network resource consumption, with the strict positivity of dynamic triggering functions theoretically proven. Finally, numerical simulations on mismatched RLC circuit systems validate the effectiveness and superiority of the proposed unified FxT synchronization framework.