Nonsingular terminal sliding mode control for time-delayed fractional-order T-S fuzzy systems based on finite-time scheme

In this paper, nonsingular terminal sliding mode control for fractional-order T-S fuzzy time-delay systems is discussed. The parameter uncertainty and external disturbance are included in the system model, meanwhile the controller design is implemented based on the finite-time concept. Firstly, a novel nonsingular terminal sliding surface which is suitable for the time-delayed fractional-order T-S fuzzy systems is proposed. It is proved that once the state trajectories of the system reach to the proposed sliding surface, they will be converged to the origin within a given finite time. Secondly, in terms of the established terminal sliding surface, a novel fractional-order sliding mode control law is introduced, which can force the closed loop dynamic error system trajectories to reach the terminal sliding surface over a finite time. Finally, using the Lyapunov stability theorem, the stability of the proposed method are proved. The proposed method is implemented for control of time-delayed fractional-order Permanent Magnetic Synchronous Motor chaotic systems with uncertain parameter and external disturbance to verify the effectiveness of the proposed fractional order nonsingular terminal sliding mode controller.