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

This paper describes a new method for generating an H_∞ 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_∞ 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 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