Finite time event-triggered consensus of variable-order fractional multi-agent systems

This paper focuses on the finite time consensus issue for variable-order fractional multi-agent systems (FMASs), where each agent is characterized by the piecewise-smooth systems. Firstly, the new variable-order fractional difference inequality and finite time stability theorem are developed, which greatly extend some existing results. Secondly, a distributed control protocol is presented, where a new triggering function and an internal dynamic variable are constructed for designing the dynamic event-triggered mechanism (DETM) to enlarge average event execution times and reduce the consumption of system resources. Thirdly, based on the developed variable-order fractional inequalities and finite time stability theorem, the considered systems achieve consensus within a finite time. Furthermore, it is proved that the Zeno phenomenon do not occur. Finally, the circuit realization approach for the designed control protocol is proposed and simulation results are provided to verify the correctness of theoretical analysis.