Adaptive sliding mode fault-tolerant control for type-2 fuzzy systems with distributed delays

In this paper, the problem of sliding-mode fault-tolerant control is addressed for a class of uncertain nonlinear systems with distributed delays and parameter perturbations. By using interval type-2 Takagi–Sugeno (T–S) fuzzy models, the nonlinear systems are formulated, of which uncertain parameters and distributed state delays are represented in a unified type-2 fuzzy framework. In order to tackle with the uncertain parameters in pre-designed membership functions, an adaptive mechanism is utilized to manage the time-varying weightings corresponding to the upper membership functions. A simple linear sliding surface subject to several solvable matrix inequalities is designed by using a reduced-order system. To guarantee the stability of the overall dynamic system, an adaptive sliding mode controller is designed, which can compensate for both uncertainties and distributed delays. Finally, a truck-trailer model system is used in simulations to verify the applicability and effectiveness of the control and estimation schemes.