In this paper, the problem of the asynchronous dissipative control is investigated for a class of discrete-time nonhomogeneous Markov jump systems. Hidden Markov model is introduced to represent the asynchronization between the designed controller and the system. On the contrary, the mode-dependent event-triggered mechanism is formulated to alleviate the burden of data transmission in the communication channel. The Lyapunov function, which is dependent on both mode and uncertain parameters, is considered to obtain the sufficient conditions that make the system with strictly --dissipative performance. Moreover, gains of the mode-dependent controller and coefficients of the event-triggered mechanism can be co-designed simultaneously. Finally, illustrative simulation and practical examples are provided to demonstrate the effectiveness of the proposed results.
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