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This paper researches the almost sure exponential leader-following consensus (ASELFC) of linear and nonlinear multi-agent systems (MASs) under semi-Markovian switching topologies (SMSTs). Differing from existing researchworks of MASs under SMSTs, we remove the restriction that every topology has a directed spanning tree (DST) rooted in the leader. Only partial switching topologies are requested to have a DST. By employing Lyapunov analysis method and stochastic technique, sufficient conditions for ASELFC are obtained. Finally, the theoretical results are applied to solve the synchronization of Chaos systems by using an example of Chua&#x2019;s circuits.

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Almost sure exponential consensus of linear and nonlinear multi-agent systems under semi-Markovian switching topologies and application to synchronization of Chaos systems