Fault-Tolerant Trajectory Tracking Control for Takagi–Sugeno Systems with Unmeasurable Premise Variables: Descriptor Approach

This paper discusses the problem of fault-tolerant tracking control (FTTC) for fuzzy nonlinear systems with unmeasurable premise variables. To simultaneously estimate the system states and the sensor faults, a fuzzy descriptor observer is developed. Then, a fault-tolerant controller to track the desired reference trajectories is synthesized. The sufficient stability conditions of the appropriate nonlinear augmented system are derived via the Lyapunov theory and the H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\infty $$\end{document} approach. In order to obtain both the observer and the controller gains the design conditions are formulated in Linear matrix inequality terms which can be solved using a one-step design procedure. Finally, the FTTC strategy is illustrated on a two-tank system to show its effectiveness.