Linear Feedback Stackelberg Equilibrium of Robust Hierarchical Difference Games

We consider a class of discrete-time hierarchical game subject to exogenous disturbance. Different from
$H_{2}/H_{\infty}$
control, the disturbance appears not only in the value functional of the leader but also in that of the follower. We introduce a linear feedback information structure to the leader, and provide necessary and sufficient conditions for the existence of the Stackelberg equilibrium. The optimal strategy is explicit obtained in terms of two decoupled and symmetric equations.