Robust Observer-Based Fuzzy Control Via Proportional Derivative Feedback Method for Singular Takagi-Sugeno Fuzzy Systems

Abstract

This paper investigates a robust observer-based control problem for uncertain nonlinear singular systems. Based on the modeling approach, the system is described by Takagi-Sugeno (T-S) fuzzy model such that the linear theories can be applied to discuss the problem. To guarantee the regularity and impulse-free property, proportional derivative (PD) control scheme and parallel distributed compensation (PDC) concept are employed to construct the fuzzy controller. Furthermore, a PD fuzzy observer is also designed to ensure the existence the derivative term of controller and to estimate the unmeasurable states. For the problem, a Lyapunov function and converting technologies are applied to derive less conservative stability criterion. Moreover, some sufficient conditions are transferred into Linear Matrix Inequality (LMI) form for using convex optimization algorithm. In addition, uncertainty is also considered for practical operation to achieve robustness of the closed loop system. According to the uncertainty and the derived conditions, a general and relaxed observer-based fuzzy controller design method is proposed to guarantee the robust asymptotical stability of the uncertain nonlinear singular systems. Finally, two numerical examples are provided to verify the applicability and availability of the proposed design method.