Second-order event-triggered adaptive containment control for a class of multi-agent systems

This paper is primarily concerned with the event-triggered adaptive containment control for the second-order linear multi-agent systems (MASs) subject to time-varying input delays. Different from traditional methods, the triggering thresholds can be time-variable and achieved online, which are regulated by the triggering error. Then the number of transmitted data is modulated by two adaptive laws that play a crucial role in deciding whether to release the current data or not. By selecting two augmented types of Lyapunov-Krasovskii functionals (LKFs) and applying three effective inequalities, these earlier ignored information can be recollected and the field of application can be greatly enlarged. Moreover, the issues on delay-dependence respectively take uniform input delay and nonuniform input ones into consideration, in which the inter-relationship among time-delays can be involved. Finally, two MAS examples are exploited to illustrate our theoretical results.