Predefined-Time Stabilization of T–S Fuzzy Systems: A Novel Integral Sliding Mode-Based Approach
Chang‐Duo Liang, Ming‐Feng Ge, Zhi‐Wei Liu, Xisheng Zhan, Ju H. Park
Abstract
This article investigates the predefined-time stabilization problems of Takagi–Sugeno (T–S) fuzzy systems. For addressing the considered problems, a class of novel integral sliding mode surface is first designed based on the time-regulator function, on which the system states are forced to converge to the origin in a predefined time after the sliding mode surface is reached. Further, the proposed sliding surface is employed to construct predefined-time integral sliding mode controller for the time delayed and disturbed T–S fuzzy system. The settling time appears as the sum of two predefined-time parameters in the controller design, which, respectively, adjusts the convergence time for reaching the sliding mode surface and the convergence time for arriving the origin from the sliding mode surface. The sufficient conditions for maintaining the predefined-time stability of the T–S fuzzy systems are obtained through systematic Lyapunov stability analysis. Finally, a numerical simulation example on delayed and disturbed Chua circuit is presented to verify the effectiveness of the proposed predefined-time integral sliding mode controller.