Robust Observer-Based Controller Design for Constrained Takagi-Sugeno Systems

Abstract

This work concerns a descriptor Takagi-Sugeno (T-S) fuzzy system. The system is subject to disturbances, sensor faults, the presence of unmeasurable premise variables, and input saturation which the latter are considered uncertainties of the system. First, the considered system is transformed into the polytopic representation, and then, a robust  Proportional-Integral (PI) observer-based controller is designed. This observer-based controller, can estimate both the system states, and the faults, and stabilize closed-loop state trajectories. An integrated robust controller strategy is adopted by a novel structure of non-Parallel Distributed Compensation (non-PDC) control law. furthermore, the proposed approach expresses the stability conditions of controller design are expressed in terms of Linear Matrix Inequalities (LMIs) constrained optimization problem. Using LMI TOOLBOX in MATLAB, we can easily design the type PI observer for efficient robust state/fault estimation and solve the  observer-based controller design problem of discrete-time T-S fuzzy systems. Finally, an application to a rolling disc process is given to illustrate the effectiveness of the proposed method.