This article focuses on the issue of reachable set estimation(RSE) with the consensus performance for multi-agent systems(MASs) under event-triggered scheme(ETS) and semi-Markov switching topologies with partially unknown rates(SMST-PUR). Firstly, through model transformation, the consensus research of MASs can be converted to the closed-loop stability analysis problem, and a periodic sampling ETS is employed to reduce the frequency of information broadcasting by the behavior of communicating with neighbors at the special moments. Secondly, the Lyapunov-Krasovskii functions(LKFs) with state information of time delay are constructed, whose goal is to capture more dynamics of time delay that impact on the controller’s design. And a group of sufficient conditions in the aspect of linear matrix inequalities(LMIs) is derived to guarantee that the states of error system can be confined within a finite union of ellipsoid-like sets corresponding to each mode with consensus manifestation under the action of switching topology randomly governed by SMST-PUR. Simultaneously, the method of co-designing the consensus controller and the triggered matrices of ETS with RSE performance is depicted to save communication resources availably. Finally, a study case is utilized to verify the validity of the proposed method and the comparative results illustrate the advantages and effectiveness of the control algorithm designed in this paper.
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