This paper addresses the problem of static output feedback synthesis and focuses on § ©¨opt imisation. The bilinear problem of finding a control feedback gain and a Lyapunov matrix is shown to be equivalent to a BMI problem that involves slack variables and a state feedback gain. This BMI condition is a promising theoretical result that links the two state and output feedback questions in a unified formulation. Based on this new expression, an efficient numerical procedure is derived. Some telling examples show that it is quite competitive compared to other algorithms proposed in the literature. Extensions to robust § ¨opt imal synthesis are derived. They show that unlike other BMI approaches, the method is of the same complexity if the system is certain or uncertain.