This paper is concerned with the control problem for different types of one-sided Lipschitz (OSL) nonlinear systems subject to input nonlinearities, unmatched polytopic uncertainties and external perturbations. The design framework gathers the high robustness qualities of the sliding mode control (SMC) and the technique. The aims is to consider the bounded disturbance attenuation measure in the analysis of sliding mode dynamics, thus to ameliorate the performance of the SMC system. An integral switching surface function is chosen and related synthesis conditions for the sliding mode dynamics are formulated in terms of linear matrix inequalities (LMIs). Then, an appropriate control law is synthesized such that reachability of the switching manifold is ensured. At last, simulation examples are provided to prove the feasibility of the proposed approach.