Dimension reduction LMI‐based design for dynamic periodic event‐triggered consensus control of multi‐agent systems with Markov switching topologies

Periodic event‐triggered control strategies are an effective way to reduce the number of sampling or controller updates and naturally avoid Zeno behavior. This paper proposes a dynamic periodic event‐triggered control strategy for multi‐agent systems (MASs) with Markov switching topologies using periodic sampled measurements of the agents' states and the topologies' modes. The challenge in the consensus analysis lies in decoupling the cross terms generated by mode‐dependent Lyapunov functional associated with different topologies. To address this, by fully leveraging the invariant properties of undirected and connected graphs to construct a time‐dependent Lyapunov functional, novel consensus criterion independent of the number of agents for MASs with Markov switching topologies is established in terms of dimension reduction linear matrix inequalities (LMIs), which significantly reduces the computational complexity associated with handling consensus in MASs with a larger number of agents. Furthermore, a co‐design method of event‐triggering parameters and controller gains for MASs is presented. Numerical simulations illustrate the effectiveness of the proposed theoretical results.