This paper investigates the finite-time \( H_{\infty } \) control problem for a class of continuous-time nonlinear Markov jump systems subject to parameter uncertainties and external disturbances. Within the event-triggered framework, a sliding mode control strategy is developed to address the asynchronous phenomenon between the system modes and the controller modes. First, an integral sliding mode surface is designed, and an asynchronous sliding mode control law is constructed to guarantee that the system state reaches on the sliding surface within a finite time and remains on it thereafter. Second, by introducing an event-triggered mechanism, the communication burden is effectively alleviated, the Zeno phenomenon is excluded, and system stability is ensured simultaneously. On this basis, Lyapunov stability theory and the linear matrix inequality approach is employed to analyze the stochastic finite-time boundedness and \( H_{\infty } \) performance of the closed-loop system over a finite-time interval. Finally, a numerical simulations and a tunnel diode circuit example are provided to verify the effectiveness and practicality of the proposed control method.
