By exploiting the Projection Lemma, this thesis provides less conservative LMI-like conditions for mixed H2 and H_inf control of continuous-time systems than those appeared in the current literature. The same technique has been extended to problems with time-invariant polytopic uncertainties. Numerical examples are illustrated to show improvement of the proposed results. Finally, an attempt is made to apply the Projection Lemma to stability analysis and design of systems with time-varying polytopic uncertainties.