A relatively simple ‘generalized’ H∞control law was recently introduced in Part 1. In Part 2, the solution of the derived H∞polynomial equations for self-tuning applications was considered in addition to the good robustness properties of the H∞closed-loop system. In this final part of the trilogy, the parameter estimation and controller calculation algorithms are described and the global convergence properties for the H∞self-tuning controller are derived. The utility of the self-tuner is demonstrated by the simulation of a ship steering system