In this paper, the output control problem for linear uncertain systems is investigated under the specific framework of quadratic stabilizability. The approach generalizes previous works to systems where both the state and input matrices suffer from structural uncertainty of norm bounded as well as interval type. The stabilizability conditions are translated into parametrical problems. The output stabilizability problem both in the static and dynamic aspects is investigated with the help of quadratic stabilizability and its dual notion ‘the quadratic detectability’. The dynamic output stabilization problem can first be formally expressed as a static one. In this case, the proposed approach does not enable us to deal with the complete uncertainty case where all the dynamic, control and output matrices are uncertain. The output dynamic compensation in the classical framework of observer design is also addressed.