Pinning dynamic complex networks by time-varying controller-vertex set

In this paper, we give a stability analysis of multi-agent system with a local pinning control algorithm for very general network topologies. These include determinately directed time varying topologies, the stochastically switching topologies. The pinned vertex set also varies with time, including deterministic and stochastic time-variations. We present sufficient conditions to guarantee the convergence of the pinning process: for the deterministic case, a time-varying pinned vertex set can stabilize the network of multi-agents with time-varying topologies if any vertex in the networks can be accessed by directed paths by at least one vertex in the pinned vertex set across all time intervals that are pre-defined; Similar results are also given for the stochastically switching case. As applications, numerical simulations based on the random waypoint model are given to verify our theoretical results.