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
L
₁
gain, is proposed and analyzed. It is proved that the
L
₁
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
L
₁
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.