  This article considers a discrete-time robust optimal control problem on
matrix Lie groups. The underlying system is assumed to be perturbed by
exogenous unmeasured bounded disturbances, and the control problem is posed as
a min-max optimal control wherein the disturbance is the adversary and tries to
maximise a cost that the control tries to minimise. Assuming the existence of a
saddle point in the problem, we present a version of the Pontryagin maximum
principle (PMP) that encapsulates first-order necessary conditions that the
optimal control and disturbance trajectories must satisfy. This PMP features a
saddle point condition on the Hamiltonian and a set of backward difference
equations for the adjoint dynamics. We also present a special case of our
result on Euclidean spaces. We conclude with applying the PMP to robust version
of single axis rotation of a rigid body.
