This paper deals with the H∞ adaptive sliding mode fault tolerant control problem for uncertain Takagi-Sugeno (T-S) fuzzy fractional order systems (FOSs) of fractional order 0<α<1 with mismatched disturbances. Adaptive laws are designed to estimate the upper bounds of the nonlinear terms. A sliding surface with reduced dimension is constructed by the method of state transformation. A sufficient condition in terms of linear matrix inequalities (LMIs) is established which guarantees the stability of the sliding motion. Then, a new control law is designed to make the resulting control system reach the sliding surface in a finite time. Both state and output feedback control forms are addressed. The proposed methods are illustrated by numerical simulations.

This paper focuses on the sliding mode control (SMC) problem for a class of uncertain singular fractional order systems (SFOSs). The uncertainties occur in both state and derivative matrices. A radial basis function (RBF) neural network strategy was utilized to estimate the nonlinear terms of SFOSs. Firstly, by expanding the dimension of the SFOS, a novel sliding surface was constructed. A necessary and sufficient condition was given to ensure the admissibility of the SFOS while the system state moves on the sliding surface. The obtained results are linear matrix inequalities (LMIs), which are more general than the existing research. Then, the adaptive control law based on the RBF neural network was organized to guarantee that the SFOS reaches the sliding surface in a finite time. Finally, a simulation example is proposed to verify the validity of the designed procedures.

In this paper, an interval type-2 fuzzy model is presented to describe the nonlinear singular fractional order systems (SFOSs) with $0<\alpha <2$. The problem of actuator and sensor fault estimation is addressed by designing a non-fragile sliding mode observer (SMO). Firstly, a new criterion is provided to analyse the admissibility of SFOSs, which does not need to divide the fractional order interval $(0,2)$ into interval $(0,1)$ and interval $[1,2)$ to study them separately. Then, by expanding the dimension of the SFOS, the non-fragile SMO and the sliding surface are constructed and the accurate estimations of faults and the SFOS state simultaneously are achieved. A new reaching law is designed, which can divide the process of the system moving to the sliding surface into three stages. Further the control law is constructed to guarantee the observation error reaches the sliding surface in finite time. Finally, three examples show the effectiveness of the proposed scheme.

In this paper, a delay-dependent admissibility analysis method and dissipative controller design are developed for a class of nonlinear time-delay descriptor systems subject to actuator saturation and L2-disturbances via a Takagi-Sugeno (T-S) fuzzy model. A less conservative admissible condition is first derived under which the system is not only regular, impulse free but also stable under certain initial conditions. The method can eliminate the impulsive behavior of a descriptor system so as to ensure the existence and uniqueness of solutions. The estimate of attraction domain is also determined in which the admissible initial states converge asymptotically to the origin. The disturbance attenuation capability is studied by designing the dissipative fuzzy controller such that the closed-loop system is admissible and holds the dissipative performance for the prescribed disturbance attenuation level and L2-disturbances. The method is more suitable for admissibility analysis and robust control synthesis. Moreover, H∞ control processes can be achieved in the same design process, which shows that the cost and time may potentially be reduced when a controller is designed for an actual physical system. Simulations are performed to validate the proposed methods and illustrate the decrease in conservativeness for a classic nonlinear system based on the T-S fuzzy time-delay descriptor model under actuator saturation and L2-disturbances. The study seeks to establish a foundation for investigating the control synthesis of T-S fuzzy time-delay descriptor systems subject to actuator saturation.