Strong consensus of convex second-order multi-agent systems with time-varying topologies

This paper addresses the strong consensus problem of convex second-order discrete-time multi-agent systems (MASs) with time-varying topologies. The convex second-order discrete-time MAS model is derived from the Langevin equation and therefore has a certain physical significance. The strong consensus here means that all the first- and second-order states converge to an identical value. Some fully distributed control protocols are designed with time-varying weights randomly chosen from an arbitrary finite set. These protocols are applicable to several cases where changing topologies may be directed or undirected, and connected or disconnected. As a special case, the condition for convex second-order MASs with fixed topologies to achieve the strong consensus is presented. Finally, two simulation examples illustrate the proposed results.