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Theory and Modern Applications

Table 1 Values Ψ for different frequency ranges [ 21 ]

From: Fault detection for switched T-S fuzzy systems in finite frequency domain

 

\(\boldsymbol {\omega\leq\varpi_{l}}\) (LF)

\(\boldsymbol {\varpi_{1}\leq\omega\leq\varpi_{2}}\) (MF)

\(\boldsymbol {\omega\geq\varpi_{h}}\) (HF)

Ψ

\(\left [{\scriptsize\begin{matrix}{} {-1} & {0} \cr {0} & {\varpi_{l}^{2}} \end{matrix}} \right ]\)

\(\left [{\scriptsize\begin{matrix}{} {-1} & {j\frac{\varpi_{1}+\varpi_{2}}{2}} \cr {-j\frac{\varpi_{1}+\varpi_{2}}{2}} & {-\varpi_{1}\varpi_{2}} \end{matrix}} \right ]\)

\(\left [{\scriptsize\begin{matrix}{} {1} & {0} \cr {0} & {-\varpi_{h}^{2}} \end{matrix}} \right ]\)