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This paper investigates the <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> consensus of linear multi-agent systems with semi-Markov switching network topologies and measurement noises. The information that each agent measures its neighbors’s has multiplicative noises. The switching of the network topologies are modeled by a semi-Markov process. Taking the external disturbance into account, <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> consensus of multi-agent systems with multiplicative noises is achieved under semi-Markov switching network topologies by using semi-Markov jump theory, stochastic theory and algebraic graph theory. Finally, simulation example is provided to illustrate the effectiveness of the theoretical results.

$H_{\infty}$ Consensus of Linear Multi-Agent Systems With Semi-Markov Switching Network Topologies and Measurement Noises