In this paper, it is shown that the observer-based control of uncertain discrete-time linear systems is conditioned by the solvability of three linear matrix inequalities that must hold simultaneously. The developed theory is then extended to Lipschitz discrete-time nonlinear systems. We show that the observer-based control problem, which is originally a non-convex issue, can be decomposed into two separate convex problems formulated as a set of numerically tractable linear matrix inequalities conditions. The new proposed linear matrix inequalities are neither iterative nor subject to any equality constraint. Illustrative examples are given to indicate the novelty and effectiveness of the proposed design.