Fast distributed average tracking in multi-agent networks: The case with general linear agent dynamics

Within the context of distributed average tracking (DAT) for multi-agent networks (MANs), the convergence rate of DAT algorithms is a key evaluation index. Practically, it is generally required to construct DAT algorithms with fast convergence rate for engineering MANs. Herein, fast DAT problem for MANs in the presence of multiple time-varying reference signals generated by linear non-autonomous systems is investigated for the first time. Compared with most existing results on DAT for MANs with multiple time-varying external signals, the present system model is much more generic and the DAT can be guaranteed in finite time. In particular, by using combined tools from the Luenberger canonical form theory of linear multivariable systems and non-smooth control theory, a new type of distributed observer is developed to estimate the average reference signal based on which a local tracking controller is skillfully designed and utilized. With the designed controller, the considered DAT can be achieved within a finite time depending on the initial states of agents. When the initial state of each individual agent is unavailable, a new type of fixedtime distributed observer for estimating the average reference signals and a local fixed-time tracking controller based on implicit Lyapunov functions are further proposed to solve the DAT problem in fixed time, which is independent of the initial states of agents. Additionally, numerical simulations are performed to verify the validity of the designed DAT algorithms.