This paper investigates the event-triggered finite-time state and output feedback \(H_{2}/H_\infty \) control problem for discrete-time stochastic mean-field systems (MFSs). Firstly, for a class of MFSs with external interference signals and stochastic white noise, the \(H_2\) and \(H_\infty \) performance functions are given, which contain some mathematical expectation terms. In order to reduce communication burden and network congestion, a novel event-triggered mechanism (ETM) is constructed, which has a minimum triggering interval to effectively avoid Zeno behavior. Next, by constructing two novel Lyapunov–Krasovskii functionals (LKFs), some sufficient conditions for stochastic MFSs to satisfy stochastic finite-time (SFT) \(H_{2}/H_\infty \) boundedness are established, and the minimum \(H_2\) performance index upper bound of the system is found. Then, the control gains for the two designed controllers and the event-triggered strategy parameters are obtained by using the linear matrix inequality (LMI) technique. Finally, the effectiveness of the proposed approach is validated through the performance of the designed controllers in a multi-particle system with 2000 interacting particles and a stochastic mean-field system.
