Second-order consensus of discrete-time multi-agent systems in directed networks with nonlinear dynamics via impulsive protocols

In this paper, we discuss the second-order consensus problem of discrete-time multi-agent systems with fixed and switching topology. Impulsive protocols are introduced for such multi-agent systems with nonlinear dynamics. The consensus problem of multi-agent systems is analyzed by algebraic graph theory and matrix theory, where a connection of impulsive control methods and network topologies is established. Our main results indicate that the second-order consensus of multi-agent systems can be achieved if the graphs of the topology are balanced and strongly connected under suitable conditions. Numerical simulations are presented to support the theoretical results.