###### Abstract  
This paper presents a new fuzzy sliding mode controller (FSMC) to improve control performances in the presence of uncertainties related to model errors and external disturbance (UAD). As a first step, an adaptive control law is designed using Lyapunov stability analysis. The control law can update control parameters of the FSMC with a disturbance estimator (DE) in which the closed-loop stability and finite-time convergence of tracking error are guaranteed. A solution for estimating the compensative quantity of the impact of UAD on a control system and a set of solutions are then presented in order to avoid the singular cases of the fuzzy-based function approximation, increase convergence ability, and reduce the calculating cost. Subsequently, the effectiveness of the proposed controller is verified through the investigation of vibration control performances of a semi-active vehicle suspension system featuring a magnetorheological damper (MRD). It is shown that the proposed controller can provide better control ability of vibration control with lower consumed power compared with two existing fuzzy sliding mode controllers. a pacs: 03.67.  
of approximated function with a high degree of flexibility. This inherent feature has meant that FL is used as a powerful tool in many control approaches [22; 23; 32]. Through using the combination of the SMC and FL, the salient advantages of each control strategy are kept during control action. For example, the fuzzy system is used to approximate unknown functions, while the sliding mode approach adds the possibility of establishing stable adaptation laws [32]. Therefore, as a type of robust controller with strong points, FSMC has been widely used in many application fields [27; 28; 29; 30; 31]. In addition, the design of a FSMC and estimator (or observer) for external disturbances can be independently carried out [15; 33]. An adaptive fuzzy SMC for nonlinear active suspension vehicle systems that was subjected to uncertainty due to time-variation of the sprung mass was studied in [25], in which the Takagi-Sugeno (T-S) fuzzy model was utilized to handle the uncertainty. More practical systems whose control signals are based on the state variables have been used in several research works [1; 12; 18; 23; 31]. For example, [PERSON] et al. showed an optimal adaptive fuzzy sliding mode controller for a class of nonlinear systems subjected to UAD [12], and the use of FL systems to approximate a plant's unknown functions was proposed in [18; 23; 31]. [PERSON] et al. have shown that controlling the system over the network may introduce different constraints and conditions [32]. Some of these constraints and conditions may cause delays in control signal, data quantization, safety, and security. One significant issue for designing a combined (or hybrid) controller using more than two different control techniques is the time varying rate of UAD. In the previous work by the authors of this current work, it was proven that when the time varying rate of UAD is increased, the quality of the controller is reduced [1; 2]. Moreover, the control system could become unstable due to external disturbances. In order to resolve the problems caused from the high rate of time-varying parameters, in this work, a new FSMC system is formulated, and its effectiveness is shown through experimental implementation to a semi-active vehicle suspension system. Consequently, the technical novelty of this work is to propose a new FSMC associated with a disturbance estimator (DE) to enhance vibration control performance under severe operating conditions. Therefore, the main technical contributions of this work are summarized as follows. (1) A new FSMC with a disturbance estimator DE (named DE-FSMC) that can adaptively identify plants via the online without complete knowledge about dynamic characteristics is formulated. The proposed controller has several features compared with the previous FSMC.