Responsiveness Analysis of Classic and Observer-Based Leader-Follower Systems

Motivated by the need to develop responsive teleoperation systems, the responsiveness performance of leader-follower systems is studied in this article. A new performance metric, the L1 gain, is proposed and analyzed. It is proved that the L1 gain changes monotonically with respect to edge weights and that it is closely related to the coherence metric of leader-follower systems. Explicit bounds are obtained for the L1 gain of classic leader-follower systems when the underlying graph is a tree or a growth-limited graph. Based on these findings, the performance of an observer-based leader-follower system is studied and conditions under which the observer-based system behaves better are obtained. Numerical experiments are also conducted showing that the observer-based leader-follower system can perform better than the classic leader-follower system for 2-D grid graphs in practical conditions. These results contribute to the design of teleoperation systems in the future.