## 4 Stability Analysis
\begin{split}\dot{V}&=\frac{\Gamma_{f_{1}}}{\gamma_{f _{1}}}\tilde{\mathbf{W}}_{f_{1}}^{T}\tilde{\mathbf{W}}_{f_{1}}+\frac{\Gamma_{ df_{1}}}{\gamma_{df_{1}}}\tilde{\mathbf{W}}_{df_{1}}^{T}\tilde{\mathbf{W}}_{df_{1}}+ \frac{\Gamma_{f_{2}}}{\gamma_{f_{2}}}\tilde{\mathbf{W}}_{f_{2}}^{T}\hat{ \mathbf{W}}_{f_{2}}+\frac{\Gamma_{g2}}{\gamma_{g_{2}}}\tilde{\mathbf{W}}_{g _{2}}^{T}\hat{\mathbf{W}}_{g_{2}}+\frac{\Gamma_{G_{1}}}{\gamma_{G_{1}}}\tilde {\mathbf{W}}_{G_{1}}^{T}\hat{\mathbf{W}}_{G_{1}}\\ &+\frac{\Gamma_{G_{2}}}{\gamma_{G_{2}}}\tilde{\mathbf{W}}_{G_{2} }^{T}\hat{\mathbf{W}}_{G_{2}}+\biggl{(}\lambda+k-\frac{1}{\kappa_{1}}\biggr{)} \sigma\varepsilon_{f_{1}}+\sigma\varepsilon_{df_{1}}+\sigma\varepsilon_{f_{2}} +\frac{1}{2}\sigma\varepsilon_{G_{1}}+\frac{1}{2}\sigma\varepsilon_{G_{2}}\\ &+\biggl{(}\lambda+k-\frac{1}{\kappa_{1}}\biggr{)}\sigma\tilde{d }_{1}+\sigma\tilde{d}_{1}+\sigma\tilde{d}_{2}-\eta_{1}|\sigma|-\eta_{2}\sigma ^{2}-\frac{1}{\kappa_{1}}\tilde{d}_{1}\tilde{\mathbf{W}}_{f_{1}}^{T}\mathbf{ h}_{f_{1}}-\frac{1}{\kappa_{1}}\tilde{d}_{1}\varepsilon_{f_{1}}\\ &-\frac{1}{\kappa_{1}}\tilde{d}_{1}^{2}+\tilde{d}_{1}\tilde{d}_{ 1}-\frac{1}{\kappa_{2}}\tilde{d}_{2}\tilde{\mathbf{W}}_{f_{2}}^{T}\mathbf{h} _{f_{2}}-\frac{1}{\kappa_{2}}\tilde{d}_{2}\varepsilon_{f_{2}}-\frac{1}{ \kappa_{2}}\tilde{d}_{2}\tilde{\mathbf{W}}_{G_{1}}^{T}\mathbf{h}_{G_{1}}-\frac {1}{\kappa_{2}}\tilde{d}_{2}\varepsilon_{G}-\frac{1}{\kappa_{2}}\tilde{d}_{ 2}^{2}+\tilde{d}_{2}\tilde{d}_{2}\end{split}  \tag{51}\]  
Based on the Cauchy-Schwarz inequality, the following inequality holds:  
\[\left(\mathbf{W}^{\text{T}}\mathbf{h}\right)^{2}\leq\left(\mathbf{W}^{\text{T }}\mathbf{W}\right)\left(\mathbf{h}^{\text{T}}\mathbf{h}\right) \tag{52}\]  
Applying [PERSON]'s inequality and (52), (51) can be transformed into  
\[ \begin{split}\dot{V}&\leq-\biggl{(}\eta_{2}-\frac{5 \lambda}{2}-\frac{5k}{2}+\frac{5}{2\kappa_{1}}-4\biggr{)}\sigma^{2}-\biggl{(} \frac{\Gamma_{f_{1}}}{2\gamma_{f_{1}}}-\frac{2\lambda_{f_{1}}}{\kappa_{1}} \biggr{)}\tilde{\mathbf{W}}_{f_{1}}^{T}\tilde{\mathbf{W}}_{f_{1}}-\frac{ \Gamma_{df_{1}}}{2\gamma_{df_{1}}}\tilde{\mathbf{W}}_{df_{1}}\\ &-\biggl{(}\frac{\Gamma_{f_{2}}}{2\gamma_{f_{2}}}-\frac{2\lambda_{ f_{2}}}{\kappa_{2}}\biggr{)}\tilde{\mathbf{W}}_{f_{2}}^{T}\tilde{\mathbf{W}}_{f_{2}}- \frac{\Gamma_{g2}}{2\gamma_{g_{2}}}\tilde{\mathbf{W}}_{g2}^{T}\tilde{ \mathbf{W}}_{g2}-\biggl{(}\frac{\Gamma_{G_{1}}}{2\gamma_{G_{1}}}-\frac{2\lambda _{G_{1}}}{\kappa_{2}}\biggr{)}\tilde{\mathbf{W}}_{G_{1}}^{T}\tilde{\mathbf{W}}_ {G_{1}}\\ &-\frac{\Gamma_{G_{2}}}{2\gamma_{G_{2}}}\tilde{\mathbf{W}}_{G_{2} }^{T}\tilde{\mathbf{W}}_{G_{2}}-\biggl{(}\frac{7}{8\kappa_{1}}-\frac{\lambda}{8 }-\frac{k}{8}-\frac{1}{2}\biggr{)}\tilde{d}_{1}^{2}-\biggl{(}\frac{1}{2\kappa_ {2}}-\frac{5}{8}\biggr{)}\tilde{d}_{2}^{2}+\frac{\Gamma_{f_{1}}}{2\gamma_{f_{1} }}W_{f_{1}M}^{2}\\ &+\frac{\Gamma_{df_{1}}}{2\gamma_{df_{1}}}W_{df_{1}M}^{2}+\frac{ \Gamma_{f_{2}}}{2\gamma_{f_{2}}}W_{f_{2}M}^{2}+\frac{\Gamma_{g2}}{2\gamma_{g_{2} }}W_{g2M}^{2}+\frac{\Gamma_{G_{1}}}{2\gamma_{G_{1}}}W_{G_{1}M}^{2}+\frac{ \Gamma_{G_{2}}}{2\gamma_{G_{2}}}W_{G_{2}M}^{2}\\ &+\biggl{(}\frac{\lambda}{2}+\frac{k}{2}+\frac{3}{2\kappa_{1}} \biggr{)}\varepsilon_{f_{1}M}^{2}+\frac{\varepsilon_{df_{1}M}^{2}}{2}+ \biggl{(}\frac{1}{2}+\frac{2}{\kappa_{2}}\biggr{)}\varepsilon_{f_{2}M}^{2}+ \biggl{(}\frac{1}{4}+\frac{2}{\kappa_{2}}\biggr{)}\varepsilon_{G_{1}M}^{2}\\ &+\frac{1}{4}\varepsilon_{G_{2}M}^{2}+\delta_{1}^{2}+\frac{ \delta_{2}^{2}}{2}\end{split}