Consensus in Markovian jump second-order multi-agent systems with random communication delay

In this study, the consensus problem for a class of second-order multi-agent systems (MASs) with Markovian characterisations is investigated. The stochastic switching topology and the random communication delay are dominated by two mutually independent Markov chains. The communication delay exists in the switching signal as well as the position information exchanges in the authors´ work. A novel consensus protocol is presented without using the neighbours´ velocity information. By performing three steps of model transformation and introducing a mapping for the two independent Markov chains, the original system is converted into an expanded analogous error system with two Markovian jumping parameters. A necessary and sufficient criterion for the mean square consensus of the Markovian jump second-order MASs with random communication delay is derived. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the theoretical result.