Abstract：Aiming at the problem that the multi-agent system structure will change randomly due to external disturbances, a mean-square consensus control algorithm is proposed for leader-follower multi-agent system when switching signals obey semi-Markov process. The stability of the control algorithm is analyzed by algebraic graph theory, the properties of the transition rate and the distribution function of the dwell time of semi-Markov procession and Lyapunov stability theory. The results show that sufficient conditions for the system to achieve mean square consensus is given by the designed impulsive control protocol. In addition, if the pulse interval has an upper bound, the mean square consensus can still be achieved. Finally, the validity of the proposed condition is verified by the numerical example.
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