Coupled stability analysis of cascaded leader–follower teleoperation networks using Möbius transformation

In this paper, we use the notion of Mobius transformation to develop a chain-wise methodology for the analysis of coupled stability in a cascade of leader-follower networks. The methodology tracks the transmission of the load passivity unit disk through the cascade to the user network. It allows for networks in the cascade that are neither passive nor absolutely stable. Due to its modularity, the proposed methodology is more suitable for dynamic distributed systems in which a network block, such as virtual coupling or delay in the cascade, is modified, added or taken out. We also introduce the notion of "bounded-(sic) absolute stability'' to verify the coupled stability for any prescribed range of loads, denoted by circles in the scattering domain. To demonstrate the effectiveness of the proposed methodologies, numerical and experimental results for a position-force control architecture under constant time delays are provided.