The event-triggered scaled consensus of multi-agent systems with semi-Markov switching topologies under partially unknown rates

For multi-agent systems(MASs), the continuous information interaction behavior between agents is normally necessary for acquiring the control feedback at each operating instant, allowing for achieving the scaled consensus in the presence of switching topologies randomly. However, consecutive communication results in high resource consumption due to frequent updating of the controllers, which poses a challenge in scenarios with limited communication resources. To address this issue, a novel error-based event-triggering scheme(ETS) with a sampling-periodic framework is developed. This ETS is formulated by defining a group of error terms, with the purpose of ensuring that the agents in MASs can realize the scaled consensus performance with either the average or proportional values, while effectively reducing the frequency of information broadcasting among agents. Specifically, the scaled consensus problem is initially transformed into a stability consideration of the reduced-order system through model transformation. Additionally, the transition rate(Tr) in semi-Markov switching process(SMSP) is considered to be incompletely unknown to capture more topology random dynamics due to the unexpected nature of the actual environment, facilitating to derive the stability conditions with reduced conservatism. And the sufficient conditions(SCs) of event-triggered scaled consensus(ETSC) are obtained in terms of linear matrix inequalities(LMIs) by employing the Lyapunov functions appropriately. Meanwhile, the scaled consensus controller(SCC) and the event-triggered matrices(ETMs) in ETS with switching sequence of topology are co-designed efficaciously to manage both the agent’s behavior and its triggering frequency. Finally, the feasibility of theoretical results is verified by using a numerical example, and the comparative results demonstrate the effectiveness of proposed method in this paper.