Centralized and decentralized event-triggered control for group consensus with fixed topology in continuous time

The communication weights in traditional consensus problems are all positive, while the communication weights in group consensus are partly real numbers. In addition, with regard to energy consumption and communication constraints, event-triggered control has advantages over periodic control. Therefore, it is of great significance to investigate group consensus based on event-triggered control. We develop two event-triggered functions to decide when to activate the control input in centralized and decentralized cases, respectively. Additionally, the infamous Zeno behavior can be excluded in the centralized case. Moreover, in the decentralized case, we simplify the event-triggered function by calculating the maximum and minimum of the corresponding parameters, so as to save memory of the systems.