Finite-time and fixed-time adaptive consensus of multi-agent systems with general linear dynamics

This paper investigates the adaptive consensus problem of general linear multi-agent systems. Finite-time consensus and fixed-time consensus are both discussed. In order to remove the dependence on global information about system topology, distributed adaptive mechanisms are introduced. Compared with the existing asymptotic consensus results, the system's convergence speed is improved by the proposed distributed finite-time consensus protocol. Furthermore, a distributed fixed-time consensus protocol is proposed to remove the dependence on system's initial state. Under the fixed-time consensus protocol, it is proved that an upper bound of the system's convergence time can be estimated. Sufficient conditions are given to ensure that all agents can achieve consensus in finite time and fixed time, respectively. Finally, the effectiveness of the proposed protocols is illustrated by a simulation example.