Integral Sliding-Mode Fault-Tolerant Control for Fuzzy Singular Systems with Actuator Saturation

In this paper, 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} reliable control problem is investigated for a class of nonlinear singular systems subject to external disturbance and actuator faults and saturations. By means of the Takagi–Sugeno fuzzy model to describe the nonlinear plant, a reliable sliding-mode control scheme is built to compensate for the impact of aforementioned factors on system stability and performance. First, a fuzzy integral sliding function is designed and sufficient conditions are derived such that the sliding-mode dynamics is robustly admissible and satisfies the pre-specified 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} disturbance attenuation requirement. Then, by considering the saturation as nonlinear input, an adaptive sliding-mode control law is synthesized to ensure reachability of the specified sliding surface. Finally, the lower-limb rehabilitation system is exploited to validate the effectiveness of the presented controller design methodology.