Incentive game approach to $H_{\infty}$ -constrained system with hierarchy decision makers

In this paper, incentive game approach is introduced to deal with
$H_{\infty}$
-constrained system. In hierarchy A, the leader derives the leader's team-optimal solution while the non-cooperative followers are induced to get the Nash equilibrium. In hierarchy B, the hierarchy A plays the leader's role while the deterministic external disturbance is the follower. It is the first attempt to formulate the optimal filtering to
$H_{\infty}$
constraint feedback Stackelberg games with hierarchical decision players. By applying matrix maximum principle in hierarchy A and hierarchy B, respectively, solutions to forward and backward equations are presented. Conditions are given to guarantee the existence and the uniqueness of the optimal solutions by using Lyapunov equation.