Extended adaptive event-triggered formation tracking control of a class of multi-agent systems with time-varying delay

This paper considers the adaptive event-triggered formation tracking control of a class of second-order multi-agent systems (MASs) with time-varying delay. Firstly, a distributed control protocol is constructed and some extended adaptive event-triggered schemes are presented, where the triggering thresholds rely on the real-time variation of the MASs but not not pre-selected constants. Then by choosing an augmented Lyapunov-Krasovskii functional (LKF), two delay-dependent criteria are formulated in terms of linear matrix inequalities (LMIs). Especially, during estimating the upper bound on LKF's derivative, since some novel integral inequalities and a new convex technique are utilized, the conservatism can be greatly reduced. Finally, two numerical examples with some simulations are provided to illustrate our methods.