Stackelberg Game Approach to Mixed H2/H∞ Problem: The Discrete-time Case

In this paper, we are concerned with the mixed $H_{2}/H_{\infty}$ control problem which is formulated as a kind of constraint optimization problems where the control input is to minimize the H2-norm subject to the $\lt p\gt H_{\infty}$-constraint dealt with by the disturbance. The main contribution is to give the strategy in terms of three decoupled equations: two Riccati equations and one Lyapunov equation. The key technique is to apply the Stackelberg game approach by treating the disturbance as the follower and the control input as the leader respectively. A numerical example is given to verify the efficiency of the proposed approach.