This paper present a two-Riccati inequality approach for the design of fixed-order H-infinity suboptimal controllers with an observer-based structure. The two Riccati inequalities are only one-way coupled and can be solved consecutively. The fixed-order controller has the structure of a fixed-order estimator of the state feedback control law in the presence of the worst-case disturbances. It retains the observed-based compensates structure of the full-order central controller of the standard H-infinity design but adds a fixed-order dynamic and mappings between the full-order and the fixed-order state spaces. In the full-order special case, this controller recovers to the minimal entropy central controller of the standard H-infinity design.