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In this paper, we present a virtual control contraction metric (VCCM) basednonlinear parameter-varying (NPV) approach to design a state-feedbackcontroller for a control moment gyroscope (CMG) to track a user-definedtrajectory set. This VCCM based nonlinear stabilization and performancesynthesis approach, which is similar to linear parameter-varying (LPV) controlapproaches, allows to achieve exact guarantees of exponential stability and$\mathcal{L}_2$-gain performance on nonlinear systems with respect to alltrajectories from the predetermined set, which is not the case with theconventional LPV methods. Simulation and experimental studies conducted in bothfully- and under-actuated operating modes of the CMG show effectiveness of thisapproach compared to standard LPV control methods.

Nonlinear parameter-varying state-feedback design for a gyroscope using virtual control contraction metrics