Consensus seeking in heterogeneous second-order multi-agent systems with switching topologies and random link failures

In this paper, we consider the issue of consensus among the agents with heterogeneous dynamics under random link failures that obey Bernoulli distribution. The heterogeneous multi-agent systems (MASs) are composed of hybrid dynamic agents including first-order dynamic agents and second-order dynamic agents, and the communication topologies are assumed to be directed and time-varying. The failure control protocol is designed by randomly utilizing the previous one- or two-step states information sent by the neighbors. A criterion for the heterogeneous consensus is established by constructing augmented systems with nonnegative random coefficient matrices for the switching topologies. With the help of graph theory and stochastic matrix theory, a sufficient condition related to switching topologies is established to ensure the realization of heterogeneous consensus. Numerical examples are finally provided to validate the theoretical result.