An Explicit Estimate for the Upper Bound of the Settling Time in Fixed-Time Leader-Following Consensus of High-Order Multivariable Multiagent Systems

In this paper, the fixed-time leader-following consensus problem is investigated for high-order multivariable multiagent systems with external disturbances. A new distributed observer is proposed for each follower under a directed information flow to estimate the leader state in a fixed time. Based on the observer, a novel tracking controller is designed such that the estimated leader state is tracked with disturbance rejection in a fixed time. Consensus conditions are established to guarantee the fixed-time stability. Different from some existing finite-/fixed-time consensus approaches, an explicit estimate for the upper bound of the settling time is derived, which provides additional system specification in advance. Moreover, for disturbance rejection, the chattering phenomenon is effectively reduced by using a distributed multivariable signum function. Finally, illustrative examples are provided to demonstrate the theoretical results.