I. Introduction
Time delay is a common phenomenon frequently encountered in real dynamic systems such as cascaded electrical networks, serial/parallel robotic systems, chemical cascaded processes, turbojet engines, traffic networks, and telecommunication systems due to measurement, transmission and transport lags, computational delays, or system inertia. The effect of time delays generally exists in output and/or system states and will result in system instability and/or performance deterioration [1]–[6], [45], [46]. Recently, adaptive fuzzy control, which incorporates a variable structure (VS) scheme, has been developed to robustly stabilize uncertain nonlinear systems (see, e.g., [7] and [8]). The main feature of such an adaptive fuzzy control with the VS scheme is its ability to deal with systems having external disturbances, time-varying system parameters, unmodeled dynamics, and nonlinearities. In complex nonlinear systems, an accurate mathematical model might not be available. Hence, fuzzy expert systems with online adjustable parameters can easily provide a valuable description of the system in terms of linguistic representation based on universal function approximators [9]–[14], [41], [44]. Fuzzy adaptive sliding mode control using output feedback control for multiple-input multiple-output nonlinear systems with unavailable states was proposed in [13] and [14]. During the past few decades, there has been rapidly growing interest in fuzzy logic control of nonlinear systems, and there have been a lot of successful applications. In particular, the technique that is based on the so-called Takagi–Sugeno (T–S) fuzzy models has attracted considerable attention [15]–[19]. The decentralized controller is proposed to deal with the problem of a class of nonlinear systems with time delay which is approximated by T–S fuzzification such that the T–S fuzzy systems are obtained [20]–[22]. In [23] and [24], a completely decentralized control was presented for a class of interconnected nonlinear systems with unknown parameters where the problem is extended to the more general case, where neither the interconnection terms nor the state are available. Tong et al. [25] designed two adaptive fuzzy output feedback control approaches for a class of uncertain stochastic nonlinear strict-feedback systems without measurement of the states. One of two adaptive fuzzy schemes was used to design an output feedback controller and the other one was designed as an observer to measure the states of stochastic nonlinear system. Furthermore, the interval type-2 fuzzy controller is viewed and used as a black-box function generator producing a desired nonlinear mapping between input and output of the controller [26]–[31]. In [32], a robust adaptive stabilizing controller was proposed for nonlinear systems with external disturbances. Some design methods for the robust stabilization of adaptive fuzzy-based control incorporating VS schemes with parameter uncertainties were presented in [9] and [33]. A robust adaptive neural-fuzzy control scheme for the position control of an -link robot manipulator including actuator dynamics was presented in [34].