The purpose of this paper is to describe systematic analysis and design tools for robust control problems with l(infinity) criteria. We first generalize the Hill-Moylan-Willems framework for dissipative systems to accommodate l(infinity) criteria, and then derive state feedback and measurement feedback synthesis procedures for l(infinity) robust control problems. The information state framework is used for the measurement feedback robust control problem. Necessary and sufficient conditions are proved, and new synthesis procedures using dynamic programming are presented.