This paper discusses two different ways, one said “direct” and the other “indirect”, leading to an observer-based H_∞ compensator. Although easily applicable to most full-order dynamic controllers (not restricted to H_∞ ones), the indirect method requires some restrictive conditions. On the other hand, the direct method is more general at the price of a more complex optimization problem. Recent progress to solve some BMI optimization problems makes the indirect method tractable and efficient with regard to the observer-based Hinfinity control design problem.