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This brief presents an output feedback controller design method for piecewise discrete-time linear systems based on a piecewise Lyapunov function and a state observer. It is shown that the resulting closed-loop system is globally stable and the controller can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software. In other words, it is shown that the separation principle of the controller and observer design is still maintained when the piecewise Lyapunov function is used. A simulation example is also given to illustrate the advantage of the proposed approach.