Event-triggered bipartite consensus for MASs on Markovian switching topologies based on distributed unknown input observer

This paper investigates the issues of event-triggered bipartite consensus for multi-agent systems (MASs) with disturbances on uncertain Markovian switching topologies, where completely unknown transition rates are considered. All designs are carried out under the assumption that the agents' states cannot be measured, and each agent can only receive output information from its neighbours. Initially, a distributed consensus variable (DCV) is constructed for each agent so that the bipartite consensus problem reduces to the convergence of the DCV. Subsequently, the dynamics of the DCV are established and characterised as an uncertain system with an accumulated disturbance. Secondly, for the DCV dynamic system, a distributed interval observer (DIO) is designed. Based on the DIO, an algebraic correlation between the accumulated disturbance and the DCV is derived. Furthermore, by using the outputs from its neighbours, a distributed unknown input observer (DUIO) is developed for each agent, which provides asymptotically converging estimates of the DCV and the accumulated disturbance. Thirdly, for the DCV system, a DUIO-based event-triggered control protocol is developed that guarantees the asymptotic stability of the DCV dynamic system. In this way, bipartite consensus for MASs is achieved. Finally, the effectiveness of the proposed method is validated through a simulation example.