Robustness and Scalability of Consensus Networks: The Role of Memory Information

It has been reported that local memory information could enhance certain consensus performance of multiagent networks, such as protecting privacy and accelerating consensus. This article aims to investigate whether memory information can improve the robustness and scalability of consensus networks. The robustness is measured by the $\ell _{2}$ gains from disturbances to consensus errors, and the scalability means that consensus can be preserved without retuning control parameters as the network scale increases. Using the linear combination of previous and current iteration states of agents and their neighbors, a memory-based consensus protocol is developed and we provide a necessary and sufficient condition for achieving consensus. Then, we establish the analytic expression of the $\ell _{2}$ gain, which is exclusively determined by control parameters and nonzero minimum and maximum Laplacian eigenvalues. Furthermore, we show how tuning the memory coefficient can improve both robustness and scalability, and the optimal control parameters are further derived. Interestingly, we observe a positive correlation between robustness and scalability.