$ H_{\infty} $ control for continuous-discrete systems in T-S fuzzy model with finite frequency specifications

Abstract

<p style='text-indent:20px;'>In this paper, the <inline-formula><tex-math id="M2">\begin{document}$ H_{\infty} $\end{document}</tex-math></inline-formula> control problem is concerned for a class of continuous-discrete T-S fuzzy systems (TSFSs) described by the Roesser model with a finite frequency (FF) specification. Assume that the frequencies of the disturbance input are known in advance and dominated within a FF range. An <inline-formula><tex-math id="M3">\begin{document}$ H_{\infty} $\end{document}</tex-math></inline-formula> performance is established within a FF range for continuous-discrete TSFSs, which is an extension of the standard <inline-formula><tex-math id="M4">\begin{document}$ H_{\infty} $\end{document}</tex-math></inline-formula> performance. This paper aims to construct a state feedback controller which guarantees the closed-loop system to be stable and to have a prescribed FF <inline-formula><tex-math id="M5">\begin{document}$ H_{\infty} $\end{document}</tex-math></inline-formula> performance. A numerical tractable method for designing a controller is obtained through matrixing, thus giving conveniently the expression of controller with linear matrix inequality as tool kit.</p>