$ H_{\infty} $ control for continuous-discrete systems in T-S fuzzy model with finite frequency specifications
Zhaoxia Duan, Jinling Liang, Zhengrong Xiang · Discrete and Continuous Dynamical Systems - S · 2022
In this paper, the \begin{document}$ H_{\infty} $\end{document} control problem is concerned for a class of continuous-discrete T-S fuzzy systems (TSFSs) described by the Roesser model with a finite frequency (FF) specification. Assume that the frequencies of the disturbance input are known in advance and dominated within a FF range. An \begin{document}$ H_{\infty} $\end{document} performance is established within a FF range for continuous-discrete TSFSs, which is an extension of the standard \begin{document}$ H_{\infty} $\end{document} performance. This paper aims to construct a state feedback controller which guarantees the closed-loop system to be stable and to have a prescribed FF \begin{document}$ H_{\infty} $\end{document} 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.