Impulsive consensus of stochastic multi-agent systems under semi-Markovian switching topologies and application

This paper studied the impulsive consensus of stochastic multi-agent systems (MASs) under semi-Markovian switching topologies. The semi-Markovian process is employed to describe the random changes of communication topologies among agents. Applying the impulsive control method, the communication among agents is only needed at impulsive control instants. For the connectivity of communication topologies, we only require that partial communication topologies contain a directed spanning tree, which remove the restriction that every communication topology contains a directed spanning tree in existing works. Using the Lyapunov function method and the stationary distribution of semi-Markovian process, the impulsive control protocol (ICP) is designed to ensure the almost surely exponential consensus of stochastic MASs. As an application, the obtained result is used to solve the secure impulsive consensus of stochastic MASs under random cyber-attacks. We proposed a novel model of random cyber-attacks, in which adversaries can destroy communication links of agents and durations of attack-active interval and attack-free interval are random variables. A simulation example is given to show the effectiveness of obtained results.