Open Access$ H_{\infty} $ control for continuous-discrete systems in T-S fuzzy model with finite frequency specifications
Author(s) -
Zhaoxia Duan,
Jinling Liang,
Zhengrong Xiang
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2022064
Subject(s) - mathematics , controller (irrigation) , discrete mathematics , algebra over a field , arithmetic , pure mathematics , agronomy , biology
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.