The problem of stabilizing uncertain discrete-time systems by observer-based control is considered. The uncertainties permitted in the systems are assumed to be structured and bounded but otherwise arbitrary. The design criterion is based on the quadratic stability of the overall closed-loop systems. By formulating the uncertainties in terms of quadratic bound matrices, a set of coupled generalized Riccati and Lyapunov equations (CGRLE) are derived. A less conservative design criterion can be obtained by recursively solving the CGRLE with the stability of the closed-loop system checked at each step. Examples are provided to illustrate the advantages of this method.