Abstract: This paper addresses the robust H_∞ control problem of uncertain linear systems with time-varying norm-bounded uncertainty in both the state and input matrices using output feedback. Necessary and sufficient conditions for robust stability with an H_∞-norm bound γ , and related necessary and sufficient conditions for robust stability with an H_∞-norm bound γ using static output feedback are derived. It is also shown that the stabilizing H_∞ controller design of a given linear uncertain system via dynamic output feedback is equivalent to that of an augmented linear uncertain system via static output feedback. For the method in this paper, only a special Riccati equation has to be solved and a numerical example is given to demonstrate the effectiveness of the proposed method.