A linear discrete time controller for spacecraft attitude dynamics on Lie group

We design a discrete-time linear controller for spacecraft attitude dynamics whose configuration space is a Lie group, by linearizing the discrete non-linear model obtained by Lie group variational integrator (LGVI) technique. The advantage, in terms of sampling rate requirement, of the proposed technique over designing a discrete-time linear controller by discretizing the linearized continuous time system model using a classical transformation technique (zero order hold) is illustrated with the help of simulation results.