The hybrid-triggered quantized H∞ control problem is investigated for discrete-time Markov jump systems (MJSs) under hybrid cyber attacks. A novel hybrid-triggered mechanism obeying Bernoulli distribution between the time-triggered mechanism and the adaptive event-triggered mechanism is introduced. The triggered condition considers the average value between current measured output and latest triggered output to avoid the unnecessary triggered data released. Meanwhile, a quantizer is adopted to optimize the data transmission rate and an observer-based controller is designed to resist the impact of deception attacks and aperiodic DoS attacks on the system. Utilizing Lyapunov stability theory and iterative methods, sufficient conditions are obtained to ensure that the closed-loop MJSs are asymptotically mean-square stable with H∞ performance. Then, an algorithm for gain matrices and triggered matrices is given. Finally, the effectiveness and availability of the proposed method are verified by a numerical example and a DC motor model.
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