Scaled consensus of multi-agent systems with switching topologies and communication noises

Abstract

This paper concerns with the mean square scaled consensus for multi-agent systems(MAS) with Markovian switching topologies and communication noises. A time-homogeneous Markov process governs the switching and each topology corresponds to a state of the process. Meanwhile, the communication noises are also considered for practical applications. We introduce a time-varying gain in control protocol which can reduce the effect of communication noises. It is shown that the effect of Markovian switching topologies mainly depends on the union of topologies associated with the positive recurrent states of Markov process. Then necessary and sufficient criteria can be established to guarantee the mean square scaled consensus under the action of distributed protocols. Moreover, the LV operator for semi-Markovian switching topologies case is derived and we can extend our result to the cases that the elements of transition rates matrix are partly unknown and the topological structure is semi-Markovian switching. Finally, an example is conducted to demonstrate the validity of our results.