Contents 1 Introduction
The increasing demands of reliability and safety for large-scale complex control systems result in many investigations of robust observer-based controller design methods for linear and nonlinear systems-see, for example, [1]–[3] and references therein. For nonlinear systems, an attractive approach is to employ Takagi-Sugeno (T-S) fuzzy model which was first proposed in [4]. The T-S multiple model structure is based on the decomposition of the operating space of the system in several zones, e.g. neighborhoods of the given operating points, and the behavior of the system in each zone is modeled as a linear subsystem. The overall fuzzy model is achieved by blending these linear subsystems with some weighting functions which are composed of the membership functions and satisfy the convex sum property. Because of the special structures of the T-S fuzzy model, it is easy for one to deal with nonlinear systems by taking advantage of the linear design technique if T-S models are constructed from nonlinear systems as design models. As a consequence, observer and robust control designs for nonlinear systems based on T-S model have gained great attention in the past decades [5]–[26]. And among these design methods, T-S model-based sliding mode control (SMC) approach [15]–[26], has become one of the major considerations recently because of SMC's significant features of high accuracy, transient response and insensitivity to variations of the system parameters and external disturbances. For instance, [15] proposed a robust sliding mode control method for T-S fuzzy models with mismatched uncertainties and external disturbances. [17] presented a new sliding mode control based on T-S fuzzy model for surface-mounted permanent-magnet synchronous motors. [19] addressed the universal integral sliding mode control problem based on T-S fuzzy models. [21] developed an adaptive integral sliding mode controller for nonlinear Markovian jump systems with partly known transition rates. [22] was devoted to design adaptive SMC for T-S fuzzy system with mismatched uncertainties and exogenous disturbances. [22] proposed a novel sliding mode control scheme for uncertain nonlinear systems that can be represented by T-S fuzzy model, aiming to eliminate the restrictive assumption that all subsystems share a common input matrix. [23] designed an adaptive sliding mode control for T-S fuzzy systems by using delta operator approach and singular value decomposition.
