Cluster Consensus for a Class of Delayed Discrete Time Multi-agent Systems

This paper investigates the cluster consensus problems for a class of delayed discrete time Multi-agent systems of the first-order and second-order, respectively. Based on the frequency-domain method and matrix theory, some algebraic criterions are proposed to ensure cluster consensus in systems affected by communication and input delay. Results show that the input time delay, the coupling weight and the coupling strength between the agents play a key role in achieving the cluster consensus, while the communication delay only affects the convergence speed of the system. Finally, the results is verified by several simulated examples.