a new observer-based adaptive fuzzy integral sliding mode controller (AFISMC) is proposed based on the Lyapunov stability theorem. The plant under study is subjected to a square-integrable disturbance and is assumed to have mismatch uncertainties both in state- and input-matrices. In addition, a norm-bounded time varying term is introduced to address the possible existence of un-modelled/nonlinear dynamics. Based on the classical sliding mode controller (SMC), the equivalent control effort is obtained to satisfy the sufficient requirement of SMC and then the control law is modified to guarantee the reachability of the system trajectory to the sliding manifold. The sliding surface is compensated based on the observed states in the form of linear matrix inequality (LMI). In order to relax the norm-bounded constrains on the control law and solve the chattering problem of SMC, a fuzzy logic (FL) inference mechanism is combined with the controller. An adaptive law is then introduced to tune the parameters of the fuzzy system on-line. Finally, by aiming at evaluating the validity of the controller and the robust performance of the closed-loop system, the proposed regulator is implemented on a real-time mechanical vibrating system.