Many design problems in control can be recast as the search for static structured (diagonal) output-feedback gains stabilizing an augmented and rearranged dynamical plant model. Moreover, in first approximation that plant may be considered as linear, or at least, one will usually request the linearized plant to be stable before considering the more complicated non-linear version. Because of the approximations leading to the linearized version, the plant parameters are usually uncertain and time-varying. In the presentation we discuss the possibility to design such static diagonal output-feedback gains for uncertain linear systems using a recently proposed matrix inequality based formulation. As expected for this hard problem, the methodology does not provide a guaranteed to succeed result, but provides some interesting promising paths for an efficient algorithm. If we have time we also mention an adaptive control strategy for updating (learning) the structured static gains.