Discrete time-delay multiagent networks: Pseudo-predictor, full-order, and reduced-order observer

This article studies the consensus and the input delay compensation problems for discrete-time linear multiagent networks with time delays in the state and input. Pseudo-predictor feedback (PPF) protocol is proposed, which makes use of the artificial closed-loop dynamics to predict the future states. Sufficient conditions are offered to guarantee the multiagent consensus on the grounds of the stability of difference equations. Full-order observer based PPF protocol and reduced-order observer based PPF protocol are simultaneously established, and it is revealed that, under the PPF protocol, the convergence rate of the states is fastest. Compared with the existent predictor feedback protocol, the proposed protocol greatly reduces the calculation burden and is easier to implement since it has no concern with the (history) input information. Finally, a numerical example is carried out to demonstrate the effectiveness of the proposed protocols.