In this chapter, we discuss the nonlinear H ∞ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315217321/5e6a8e3d-7f1f-4a8e-b362-f0f8cf29bc56/content/eq2164.tif"/> sub-optimal control problem for discrete-time affine nonlinear systems using both state and output measurement-feedbacks. As most control schemes are implemented using a digital controller, studying the discrete-time problem leads to a better understanding of how the control strategy can be implemented on the digital computer, and what potential problems can arise. The study of the discrete-time problem is also important in its own right from a system-theoretic point of view, and delineates many different distinctions from the continuous-time case.