Consensus of delayed multi-agent systems by reduced-order observer-based truncated predictor feedback protocols

For high-order linear multi-agent systems with large input and communication delays, a predictor feedback approach is established to design reduced-order observer-based output feedback protocols. This approach can compensate arbitrarily large delays but will lead to infinite dimensional protocols. Under the assumption that the open-loop dynamics is at most polynomially unstable, the proposed predictor feedback protocols is truncated by removing the distributed terms, resulting in a finite dimensional reduced-order observer-based output feedback protocols, which will be referred to as truncated predictor feedback (TPF) protocols. Compared with the predictor feedback protocols, the main advantage of the TPF protocols is that it is very easy to implement. Two numerical examples are worked out to demonstrate the effectiveness of the proposed approaches.