Integral Sliding Mode Control for Singularly Perturbed Systems with Mismatched Disturbances

This paper presents a novel integral sliding mode control (ISMC) for singularly perturbed systems (SPSs) with mismatched disturbances. A singular perturbation parameter ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon $$\end{document}-dependent disturbance observer is constructed to estimate the disturbances. An ISMC which incorporates the disturbance vector estimate is designed, such that the reachability condition is guaranteed. In order to compensate the effect of mismatched components of the disturbances extracted by the projection matrix theory, 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} control theory is employed to determine the gain of ISMC by solving a set of linear matrix inequalities. As a result, the closed-loop SPSs under the ISMC are internally exponentially stable with 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} performance index guaranteed. Finally, the effectiveness and advantages of the proposed method are demonstrated by two examples.