Group tracking control of second-order multi-agent systems with fixed and Markovian switching topologies

This paper studies the group consensus tracking issues of discrete time second-order multi-agent systems (MASs) with directed fixed and Markovian switching topologies, respectively. For MASs with m leaders, we first introduce a method to divide the whole MASs into m subgroups. Based on the subgroup-divided method, the condensation directed graph G of the communication topology of the whole MASs becomes a directed acyclic graph (DAG). Then, for MASs with fixed/Markovian switching topology, some sufficient/necessary and sufficient group consensus tracking criteria are established. Finally, simulation examples are given to illustrate the effectiveness of our results.