Retraction Notice: Robustness Margins for Attainable Consensusability of Unstable Multi-Agent Systems: Output Consensus Protocols Over Directed Network Topology

In this article, we deliver analytical expressions to characterize the attainable consensusability of a linear unstable multi-agent system (MAS). The considered MAS undergoes uncertainty variations and non-minimum phase dynamics, whose interaction topology is delineated by a communication network with a directed spanning tree. Our primary objective is to compute the maximal robustness consensus margins, which can clearly describe how communication network connectivity, the control protocols, and the system's dynamics exert influences on allowable robustness consensus in the framework of output feedback control. Towards this aim, we resolve the robust consensus problem along the spirit of the gain and phase margin problems, which amounts to handling two constrained optimization problems over feasible regions based on the stability analysis theorem of the MAS characteristic polynomials. We finally formulate explicit conditions and analytical expressions of achieved robustness consensus margins, wherein the results show the restrictions of the agent's unstable pole, non-minimum phase zero, and network connectedness on the robustly achieved gain and phase consensus margins.