This paper describes a new method for generating an H-infinity controller for a nonlinear system whose nonlinearities are modeled as describing functions. It is a three-step approach : modeling (using the describing function approach), synthesis (using the H-infinity loop shifting technique), and robustness analysis (using the labeling technique of simplicial algorithms). The method is first demonstrated by designing an optimal H-infinity controller for a first-order linear unstable system driven by a Bang-Bang actuator. A more complex example is used next to demonstrate loop shifting and simplicial algorithms as applied to a suboptimal problem. This system was implemented on a digital computer and in analog circuit form to demonstrate the practicality of the method.