Mixed H 2 / H ∞ control for discrete-time systems with input delay

This study is concerned with the mixed H 2 / H ∞ control problem under an open-loop information pattern with input delay. Compared with the delay-free case, one of the main difficulties is the non-causality caused by the time delay in the control input. The mixed H 2 / H ∞ control problem is reformulated as a leader–follower game and the Stackelberg strategy based on the maximum principle is introduced to deal with this. By introducing two co-states to capture the future information and one new state to capture the past effects, the problem can be addressed. The controllers are designed by solving the symmetric and decoupled Riccati equations. Necessary and sufficient conditions that guarantee the existence and uniqueness of the solution are proposed in this study.