In this paper we present a new control approach based on both: Linear Matrix Inequalities and Sliding Mode Control. This strategy is applied to interconnected systems which consider local disturbances (matched and unmatched disturbances) together with local and remote uncertainties. The proposed approach guarantees global stability by using only an output feedback. The control law is composed by two parts: The first one concerns a linear control feedback that is conceived to reject disturbances ( and /or uncertainties) and guarantee global stability. The control law is Linear Matrix Inequalities based strategy (multi-criteria). The second one term is conceived to increase stability robustness with respect to matched uncertainties and disturbances. This controller is designed by using a nonlinear sliding mode control law. The global stability is provided under certain (sufficient) conditions. Simulation results on a multivariable nonlinear system illustrate the behavior of the proposed approach.