This paper is concerned with the use of genetic algorithms for robust control synthesis, in a context where there is no convex formulation for such design. For that aim, a robustness analysis condition is given in terms of a linear matrix inequality feasibility problem, producing less conservative results than recent parameter dependent Lyapunov based methods (which encompasses quadratic stability) for polytopic uncertainties in linear systems. Since the design criterion is a closed-loop test formulated in the controller parameter space, any control structure constraint is allowed, such as: low-order dynamic controllers, static output feedback controllers, decentralized control, etc. The role of genetic algorithms for the design of “less conservative” and “structure-constrained” controllers is discussed.