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This paper is concerned with the event-triggered anti-disturbance control of Markov jump systems with general transition probabilities. The associated multiple disturbances cover matched and unmatched cases. Two dynamic triggering mechanisms are constructed by utilizing the tanh -function to adjust thresholds varying with input error. An adaptive disturbance observer is presented in terms of a row-by-row configuration to estimate unknown matched disturbance. According the mechanisms, corresponding composite state-feedback controllers are proposed by integrating threshold bound and adaptive estimation. Resorting to the Lyapunov stability theory and the stochastic analysis technique, the resulted closed-loop system is stochastically bounded with the required H ∞ performance. A structured separation method is utilized to solve the controller gain in terms of linear matrix inequalities. Finally, the validity of proposed schemes is verified by a numerical simulation comparison. [ABSTRACT FROM AUTHOR]