<p>This research explores the leader–follower consensus problem in semi-Markovian jump multi-agent systems with a semi-Markovian switching topology. The structural and parameter variations of the system itself are modeled using semi-Markov processes, which are also employed to describe the switching of communication topologies among agents. Compared to traditional Markovian switching topologies, this approach demonstrates stronger applicability. To avoid wasting network resources in multi-agent systems, an improved dynamic event-triggered protocol is introduced, and a consensus control protocol is designed. By constructing Lyapunov functions and utilizing continuous local martingales, sufficient conditions for achieving leader–follower exponential consensus are derived. Notably, these conditions permit the disconnection of certain communication topology graphs, thus removing the requirement for all graphs to be unilaterally connected digraphs. This result is further applied to a network attack model. Compared with existing results, the problems investigated in our study are not only better suited for complex scenarios but also demonstrate stronger practical relevance and greater extensibility. The effectiveness of our findings is corroborated by simulation examples.</p>