Adaptive Control for a Class of Switched Linear Systems Using State-Dependent Switching

In this paper, the problem of adaptive control for a class of continuous-time switched linear systems is studied using a state-dependent switching method. All subsystems of the switched system under study can be unstable. First, an adaptive controller and a variable structure (VS) switching law with sliding sector are proposed, and some conditions are established in terms of linear matrix inequalities to guarantee the underlying system to be asymptotically stable. Then the problem of robust 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 for the systems under study is also solved by designing a proposed adaptive controller and a VS switching law. Finally, a numerical example is given to demonstrate the effectiveness of the obtained theoretical results.