H∞ control of nonlinear systems using describing functions and simplicial algorithms

A novel method for generating the optimal H_∞ controller for a nonlinear system is discussed. It is a three-step approach encompassing modeling (using the describing function approach), synthesis (using the H_∞ loop shifting technique), and robustness analysis (using the labeling technique of simplicial algorithms). The method is first demonstrated by designing an optimal H_∞ controller for an unstable system driven by a bang-bang actuator. This system was implemented on a digital computer and in analog circuit form to demonstrate the practicality of the method