This chapter will consider two discrete time mixed LQR/ H∞ control problems. One is the discrete time state feedback mixed LQR/ H∞ control problem, another is the non-fragile discrete time state feedback mixed LQR/ H∞ control problem. Motivation for mixed LQR/ H∞ control problem is to combine the LQR and suboptimal H∞ controller design theories, and achieve simultaneously the performance of the...