This paper uses the concept of D-stability to place the eigenvalues of the linear component of both the controller and observer within separate circular regions in order to design a robust dynamic feedback controller using linear matrix inequality (LMI) techniques to accommodate Lipschitz type nonlinearities for continuous-time systems. Given a feasible result for both the controller and observer design, the regions will be separated in such a way that the state estimation error goes to zero much faster than the state while guaranteeing stability. This design technique is extended to incorporate the H2-norm property. The method is applied to two nonlinear systems to illustrate the design procedure.