  We propose a new central synergistic hybrid approach for global exponential
stabilization on the Special Orthogonal group SO(3). We introduce a new
switching concept relying on a central family of (possibly) non-differentiable
potential functions that enjoy (as well as their gradients) the following
properties: 1) being quadratic with respect to the Euclidean attitude distance,
and 2) being synergistic with respect to the gradient's singular and/or
critical points. The proposed approach is used to solve the attitude tracking
problem, leading to global exponential stability results.
