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In this paper, a design framework for synthesizing sliding-mode output-feedback controllers for plants with matched and mismatched uncertainties is presented. Static-output-feedback (SOF) and compensator-based sliding-mode controllers are proposed. The switching-surface design problem is formulated in terms of linear matrix inequalities (LMIs) from a polytopic perspective, as an SOF problem with mismatched uncertainties. The control law consists of linear and nonlinear components. A convex subset of the complex left half-plane is defined by the designer in order to place the closed-loop eigenvalues when synthesizing numerically the linear component using LMIs through a polytopic formulation. The nonlinear part takes into account matched uncertainties or nonlinearities. Design studies demonstrate the efficacy of the proposed controllers.