  In this paper, we present a virtual control contraction metric (VCCM) based
nonlinear parameter-varying (NPV) approach to design a state-feedback
controller for a control moment gyroscope (CMG) to track a user-defined
trajectory set. This VCCM based nonlinear stabilization and performance
synthesis approach, which is similar to linear parameter-varying (LPV) control
approaches, allows to achieve exact guarantees of exponential stability and
$\mathcal{L}_2$-gain performance on nonlinear systems with respect to all
trajectories from the predetermined set, which is not the case with the
conventional LPV methods. Simulation and experimental studies conducted in both
fully- and under-actuated operating modes of the CMG show effectiveness of this
approach compared to standard LPV control methods.
