A design procedure is presented for linear systems with inaccessible states and large parameter variations. A nominal observer structure is used in the feedback loop. The design parameters are the observer gain matrix and the estimated-state feedback matrix. The prime design objectives are an asymptotically stable closed-loop system and a minimal upper bound on an integral-quadratic performance measure. A modified performance measure is introduced which, while only indirectly related to the prime design objectives, yields a computationally feasible algorithm for the design parameters. This work extends the observer-feedback theory developed by Newmann, Rom and Sarachik, and others, for systems with no uncertainty to systems with parameter uncertainty.