Accelerated consensus of discrete-time multi-agent systems under switching topologies

Accelerated consensus problem of discrete-time multi-agent systems under directed and switching topologies is studied. In light of a vector whose norm equals to the norm of the consensus state, the sufficient conditions to achieve consensus in norm and accelerated consensus in norm are provided, respectively. Furthermore, the algorithms to obtain protocols are presented and the consensus function is formulated in norm. Finally, the numerical example is presented to show the effectiveness of these theorems.