To gain more insight into the performance of state-of-the-art Static Output Feedback (SOF) controller synthesis methods for H∞-control, quantitative comparisons are made between Lyapunov methods and well-known established non-smooth optimization methods, i.e. Hinfstruct and HIFOO. Three methods were deemed to be the most promising to compete and were bundled into one toolbox named SOFHi. The algorithms were extended to incorporate structured SOF and a variant of SOFHi was proposed to significantly improve upon the computational efficiency of the original implementation. Extensive comparisons show that SOFHi was able to compete with the established non-smooth methods and even able to significantly outperform one of them. Lastly, an elaborate flight control benchmark example is given to showcase the effectiveness of the algorithms, which involves the design of a gain-scheduled normal acceleration Control Augmentation System (CAS) for a highly maneuverable fighter aircraft.