For a class of conic-type non-linear time-delay Markov jump systems, the asynchronous dissipative output feedback controller based on the guaranteed cost control and quantiser is designed in this study. In real applications, the system and the controller modes are always non-synchronous, so we introduce the hidden Markov model to solve this problem. Furthermore, we define three novel auxiliary variables and use quantisers to accomplish the output feedback controller design. Then, the finite-time boundedness and strict dissipativity of the closed-loop systems are guaranteed by sufficient conditions, and the controller also meets the guaranteed cost-control performance. By solving a set of linear matrix inequalities, we get the controller gains, the guaranteed cost control performance index J * , and the dissipative performance index α. Finally, the correctness and feasibility of this designed approach are demonstrated by a given example.

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