To deal with the asynchronous problem of system modal and controller modal of heterogeneous multi-agent systems caused by complex network attacks, physical limitations and other factors, ensure the consistency of multi-agent systems, and improve the security of system operation. This paper proposes a design method of output feedback controller based on dissipative performance. Aiming at the situation that the state cannot be measured in the actual project, a more practical output feedback control is adopted, and a distributed dynamic compensator is designed. Combined with the output adjustment technology, the heterogeneous multi-agent system is constructed as a closed-loop error system. The hidden Markov model is used to describe the asynchronous phenomenon between multi-agent system and controller, and a double-chain Markov jump model is formed. The stochastic stability and strictly (D,E,F)-α dissipativity conditions of closed-loop error system are given by the Lyapunov stability analysis method, and the output consistency of heterogeneous multi-agent system is realized. Furthermore, a gain design method is obtained by transforming the gain design of asynchronous controller with dissipative properties into a set of feasible solutions of linear matrix inequalities. Finally, a simulation example verifies the effectiveness of the control algorithm proposed in this paper. The results show that compared with the existing results, the dissipative asynchronous controller based on output feedback designed in this paper has good compatibility with various multi-agent systems. At the same time, there are still many technical problems that need to be solved urgently. With the development of science and technology, smoother network communication methods and sensitive sensor networks can be used as references for breakthroughs of key issues in the field of multi-agent collaborative control in the future.