This paper is concerned with the fixed-time average consensus problem of
delayed multi-agent systems (MASs) under the framework of discontinuous
inherent dynamics. By introducing the weighted average state as the
virtual leader, the leaderless fixed-time consensus problem can be
transformed into the stability problem of the error system. Two
distributed control protocols are skillfully proposed based on the
neighbors’ information to guarantee that the MASs can achieve finite-
and fixed-time consensus, respectively. By establishing a relationship
between any two nodes in the MASs, some sufficient conditions are
derived such that the resulting consensus tracking errors can be
converged to zero within a finite/fixed time, respectively. In addition,
an analytical expression of the setting time is given, which does not
rely on the initial conditions. Moreover, finite-/fixed-time control
under switching topology is also studied, and the relevant results are
achieved. The theoretical results are illustrated by two examples.