Observer-Based Sliding Mode Control for T–S Fuzzy Descriptor Systems With Time Delay

This paper examines the problem of observer-based sliding mode control designs for a class of descriptor Takagi-Sugeno fuzzy systems with time delay and uncertainties. Specifically, based on the detailed discussions on the existence conditions, a reduced-order robust observer is designed first where the influences of the uncertainties are totally removed. Second, by choosing appropriate coordinate transformations and matrix decompositions, an actual and a virtual sliding mode variables are constructed, and an observer-based sliding mode controller is developed to handle the uncertainties such that the virtual sliding mode surface can be reached and maintained in a finite time, whereas the actual sliding mode variable approaches to zeros asymptotically. And then, we prove that the system asymptotic stability can be guaranteed after the virtual sliding mode surface has been reached or the actual sliding mode variable approached to zero. In addition, the existence conditions for both the observer and the sliding mode controller are given in strict linear matrix inequality forms. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.