Observer-based adaptive control and faults estimation for T-S fuzzy singular fractional order systems

This paper handles the issue of adaptive control and faults estimation of a class of T-S singular fractional order systems(SFOSs) with 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} performance, where the fractional order belongs to (0, 1). Firstly, a novel observer for SFOSs is proposed, which estimate unmeasurable or partially measurable state and faults, simultaneously. Secondly, regarding to the information obtained by the above observer and the designed adaptive parameters, an adaptive controller is proposed to estimate actuator faults of the SFOSs. Further, it is indispensable to ensure the admissibility of the proposed fuzzy SFOSs with 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} performance, novel sufficient conditions are obtained by linear matrix inequalities (LMIs), Finally, to illustrate the method proposed above is available, simulation examples are presented.