  The finite horizon $H_2/H_\infty$ control problem of mean-field type for
discrete-time systems is considered in this paper. Firstly, we derive a
mean-field stochastic bounded real lemma (SBRL). Secondly, a sufficient
condition for the solvability of discrete-time mean-field stochastic
linear-quadratic (LQ) optimal control is presented. Thirdly, based on SBRL and
LQ results, this paper establishes a sufficient condition for the existence of
discrete-time stochastic $H_2/H_\infty$ control of mean-field type via the
solvability of coupled matrix-valued equations.
