Consensus of multi-agent systems with finite-time and fixed-time observation

This paper addresses the distributed control problem of single-input high-order multi-agent systems (MASs). Firstly, a nonlinear observation system is proposed to track the target system in a finite-time, and a distributed event-triggered protocol is designed to reduce the frequency of data transmission. Moreover, we popularize the distributed event-triggered algorithm to general directed networks. Applying the tree-type error method and implicit Lyapunov functions, some criteria are derived to ensure the finite-time observation and asymptotical consensus. Furthermore, based on single-output state, a fixed-time nonlinear observer is introduced, and the asymptotical consensus is also considered utilizing the distributed event-triggered protocol. Finally, the effectiveness of the control strategies is demonstrated via some numerical simulations.