## 3 System Model
### Model Analysis
\begin{array}{cccccccc}\bar{\beta}_{2}\bar{f}\delta&\bar {f}(\theta\beta_{2}+\eta\bar{\beta}_{2})&\bar{f}\alpha_{11}(\alpha_{2}\beta_{2 }+\bar{\alpha}_{2}\bar{\beta}_{2})&\bar{\beta}_{2}f\delta&f(\theta\beta_{2}+ \eta\bar{\beta}_{2})&f\alpha_{11}(\alpha_{2}\beta_{2}+\bar{\alpha}_{2}\bar{ \beta}_{2})\\ 0&\bar{f}(\theta\beta_{12}+\alpha_{2}\bar{\beta}_{12})&\beta_{12}\bar{f}\alpha_{ 11}\alpha_{2}&0&f(\theta\beta_{12}+\bar{\alpha}_{11}\alpha_{2}\bar{\beta}_{12} )&f\alpha_{11}\alpha_{2}\\ 0&\beta_{11}\bar{f}\theta&\bar{f}\alpha_{2}(\alpha_{11}\beta_{11}+\bar{\beta}_{11 })&0&\beta_{11}f\theta&f\alpha_{2}(\alpha_{11}\beta_{11}+\bar{\beta}_{11})\\ r\delta&r\eta&r\alpha_{11}\bar{\alpha}_{2}&\bar{r}\delta&r\eta&\bar{r}\alpha_{ 11}\bar{\alpha}_{2}\\ 0&r(\theta e_{12}+\alpha_{2}\bar{e}_{12})&e_{12}r\alpha_{11}\alpha_{2}&0&\bar{r}( \theta e_{12}+\bar{\alpha}_{11}\alpha_{2}\bar{e}_{12})&\bar{r}\alpha_{11}\alpha_{2 }\\ 0&e_{11}r\theta&r\alpha_{2}(\alpha_{11}e_{11}+\bar{e}_{11})&0&e_{11}r\theta&r \alpha_{2}(\alpha_{11}e_{11}+\bar{e}_{11})\end{array} \right) \tag{10}\]\[H_{k,k+1}=\left( \begin{array}{cccccc}\bar{\beta}_{2}\bar{f}\theta&\bar{\beta}_{ 2}\bar{f}\alpha_{11}\alpha_{2}&0&\bar{\beta}_{2}f\theta&\bar{\beta}_{2}f\alpha _{11}\alpha_{2}\\ 0&0&0&0&0&0\\ 0&0&0&0&0&0\\ r\theta&r\alpha_{11}\alpha_{2}&0&r\theta&\bar{r}\alpha_{11}\alpha_{2}\\ 0&0&0&0&0\\ 0&0&0&0&0\end{array} \right) \tag{11}\]  
4. The remaining non-zero submatrices in matrix \(H\) are represented as Equations (12)-(15). \[H_{k,k}=\left( \begin{array}{cccccc}\bar{f}(\delta\beta_{2}+\bar{\varsigma} \beta_{2})&\beta_{2}\bar{f}\eta&\beta_{2}\bar{f}\alpha_{11}\alpha_{2}&f(\delta \beta_{2}+\bar{\alpha}_{11}\bar{\alpha}_{12}\bar{\beta}_{2})&\beta_{2}f\eta& \beta_{2}f\alpha_{11}\alpha_{2}\\ \beta_{12}\bar{f}\delta&\bar{f}(\eta\beta_{12}+\bar{\kappa}_{2}\bar{\beta}_{ 12})&\beta_{12}\bar{f}\alpha_{11}\bar{\kappa}_{2}&\beta_{12}f\delta&f(\eta \beta_{12}+\bar{\kappa}_{11}\bar{\kappa}_{2}\bar{\beta}_{12})&f\alpha_{11} \bar{\kappa}_{2}\\ \beta_{11}\bar{f}\delta&\beta_{11}\bar{f}\eta&\bar{f}\bar{\kappa}_{2}(\alpha _{11}\beta_{11}+\bar{\beta}_{11})&\beta_{11}f\delta&\beta_{11}f\eta&f\bar{ \kappa}_{2}(\alpha_{11}\beta_{11}+\bar{\beta}_{11})\\ r\zeta&0&r\bar{\kappa}_{11}\bar{\kappa}_{12}&0&0\\ \epsilon_{12}r\delta&r(\eta\epsilon_{12}+\bar{\kappa}_{2}\epsilon_{12})& \epsilon_{12}r\alpha_{11}\bar{\kappa}_{2}&\epsilon_{12}r\delta&r(\eta\epsilon _{12}+\bar{\kappa}_{11}\bar{\kappa}_{2}\epsilon_{12})&r\alpha_{11}\bar{ \kappa}_{2}\\ \epsilon_{11}r\delta&\epsilon_{11}r\eta&r\bar{\kappa}_{2}(\alpha_{11}\epsilon_ {11}+\bar{\epsilon}_{11})&\epsilon_{11}r\delta&\epsilon_{11}r\eta&\bar{ \kappa}_{2}(\alpha_{11}\epsilon_{11}+\bar{\epsilon}_{11})\end{array} \right) \tag{12}\]  
\[H_{k,k+1}=\left( \begin{array}{cccccc}\bar{\beta}_{2}\bar{f}\delta&\bar{f}( \theta\beta_{2}+\bar{\alpha}_{11}\alpha_{12}\bar{\beta}_{2})&\bar{f}\alpha_{ 11}(\alpha_{2}\beta_{2}+\bar{\beta}_{2})&0&f(\theta\beta_{2}+\bar{\alpha}_{11} \alpha_{12}\bar{\beta}_{2})&f\alpha_{11}(\alpha_{2}\beta_{2}+\bar{\beta}_{2}) \\ 0&\bar{f}(\theta\beta_{12}+\alpha_{2}\bar{\beta}_{12})&\beta_{12}\bar{f}\alpha _{11}\alpha_{2}&0&f(\theta\beta_{12}+\bar{\kappa}_{11}\alpha_{2}\bar{\beta}_{ 12})&f\alpha_{11}\alpha_{2}\\ 0&\beta_{11}\bar{f}\theta&\bar{f}\alpha_{2}(\alpha_{11}\beta_{11}+\bar{\beta}_ {11})&0&\beta_{11}f\theta&f\alpha_{2}(\alpha_{11}\beta_{11}+\bar{\beta}_{11}) \\ r\delta&r\bar{\kappa}_{11}\alpha_{12}&r\alpha_{11}&0&\bar{r}\bar{\kappa}_{11} \alpha_{12}&\bar{r}\alpha_{11}\\ 0&r(\theta\epsilon_{12}+\alpha_{2}\bar{\epsilon}_{12})&\epsilon_{12}r\alpha _{11}\alpha_{2}&0&r(\theta\epsilon_{12}+\bar{\kappa}_{11}\alpha_{2}\bar{ \epsilon}_{12})&\pi\alpha_{11}\alpha_{2}\\ 0&\epsilon_{11}r\theta&r\alpha_{2}(\alpha_{11}\epsilon_{11}+\bar{\epsilon}_{11 })&0&\epsilon_{11}r\theta&\pi\alpha_{2}(\alpha_{11}\epsilon_{11}+\bar{ \epsilon}_{11})\end{array} \right) \tag{13}\]  
\[H_{k+1,k}=\left(