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This paper considers the development of sliding-mode-based output-feedback controllers for uncertain systems which are subject to time-varying state delays. A novel method is proposed for design of the switching surface. This method is based on the descriptor approach and leads to a solution in terms of linear matrix inequalities (LMIs). When compared to existing methods (even for systems without delays), the proposed method is efficient and less conservative than other results, giving a feasible solution when the Kimura-Davison conditions are not satisfied. No additional constraints are imposed on the dimensions or structure of the reduced order triple associated with design of the switching surface. The magnitude of the linear gain used to construct the controller is also verified as an appropriate solution to the reachability problem using LMIs. A stability analysis for the full-order time-delay system with discontinuous right-hand side is formulated. This paper facilitates the constructive design of sliding-mode static-output-feedback controllers for a rather general class of time-delay systems. A numerical example from the literature illustrates the efficiency of the proposed method.