The paper presents a Riccati equation approach to the output feedback quadratic stabilisation of an uncertain system. The uncertain systems under consideration depend on a norma-bounded time-varying matrix of uncertain parameters. A feature of the approach taken is that it involves the minimisation of a certain bound on an LQG cost function. The results were obtained by combining recent results on an optimal guaranteed cost linear quadratic regulator problem for uncertain systems and an optimal guaranteed cost state estimation problem for uncertain systems.