  Synergistic hybrid feedback refers to a collection of feedback laws that
allow for global asymptotic stabilization of a compact set through the
following switching logic: given a collection of Lyapunov functions that are
indexed by a logic variable, whenever the currently selected Lyapunov function
exceeds the value of another function in the collection by a given margin, then
a switch to the corresponding feedback law is triggered. This kind of feedback
has been under development over the past decade and it has led to multiple
solutions for global asymptotic stabilization on compact manifolds. The
contributions of this paper include a synergistic controller design in which
the logic variable is not necessarily constant between jumps, a synergistic
hybrid feedback that is able to tackle the presence of parametric uncertainty,
backstepping of adaptive synergistic hybrid feedbacks, and a demonstration of
the proposed solutions to the problem of global obstacle avoidance.
