## 2 Problem Formulation and Preliminary  
### Problem Statement  
In this paper, the attitude model of RLV in the reentry phase is described as follows [12]:  
\[\left\{ \begin{array}{l}\dot{\alpha}=\frac{\sin\sigma}{\cos\beta}\Big{[}\dot{ \psi}\cos\gamma-\dot{\theta}\sin\psi\sin\gamma+(\dot{\varphi}+\omega_{\text{E} })(\cos\theta\cos\psi\sin\gamma-\sin\theta\cos\gamma)\Big{]}\\ \quad-\frac{\cos\sigma}{\cos\beta}\Big{[}\dot{\gamma}-\dot{\theta}\cos\psi-( \dot{\varphi}+\omega_{\text{E}})\cos\theta\sin\psi\Big{]}\\ \quad-p\cos\alpha\tan\beta+q-r\sin\alpha\tan\beta\\ \dot{\beta}=\ p\sin\alpha-r\cos\alpha+\sin\sigma\Big{[}\dot{\gamma}-\dot{ \theta}\cos\psi+(\dot{\varphi}+\omega_{\text{E}})\cos\theta\sin\psi\Big{]} \\ \quad+\cos\sigma\Big{[}\dot{\psi}\cos\gamma-\dot{\theta}\sin\psi\sin\gamma-( \dot{\varphi}+\omega_{\text{E}})(\cos\theta\cos\psi\sin\gamma-\sin\theta\cos \gamma)\Big{]}\\ \dot{\sigma}=-p\cos\alpha\cos\beta-q\sin\beta-r\sin\alpha\cos\beta+\dot{\alpha }\sin\beta-\dot{\psi}\sin\gamma\\ \quad-\dot{\theta}\sin\psi\cos\gamma+(\dot{\varphi}+\omega_{\text{E}})(\cos \theta\cos\psi\cos\gamma+\sin\theta\sin\gamma)\\ \dot{\vartheta}=\frac{I_{2x}M_{x}}{I_{xx}I_{x}-I_{xx}^{2}}+\frac{I_{xx}M_{x}}{I _{yx}I_{x}I_{x}-I_{xx}^{2}}+\frac{(I_{xx}-I_{yy}I_{x}+I_{xx})I_{xz}}{I_{xx}I_ {x}-I_{xx}^{2}}pq+\frac{(I_{yy}-I_{zz})I_{xz}-I_{xx}^{2}}{I_{xx}I_{x}-I_{xx}^{2 }}qr\\ \dot{q}=\frac{M_{y}}{I_{yy}}+\frac{I_{zz}(r^{2}-p^{2})}{I_{yy}}+\frac{(I_{zz}-I _{xx})I_{xx}}{I_{x}I_{x}-I_{xx}^{2}}pr\\ \dot{r}=\frac{I_{xx}M_{x}}{I_{xx}I_{x}-I_{xx}^{2}}+\frac{I_{xx}M_{x}}{I_{xx}I_{ x}-I_{xx}^{2}}+\frac{(I_{xx}-I_{yy}+I_{xx})I_{xz}}{I_{xx}I_{x}-I_{xx}^{2}}pq+ \frac{(I_{yy}-I_{zz}-I_{xx})I_{xz}}{I_{xx}I_{x}-I_{xx}^{2}}qr\end{array} \right. \tag{1}\]  
where \(\theta\) and \(\varphi\) represent the latitude and the longitude, respectively. \(q\), \(r\), and \(p\) are the pitch angular rate, yaw angular rate, and roll angular rate, respectively. \(\beta\), \(\alpha\), and \(\sigma\) represent the sideslip, attack, and bank angles, respectively. \(\psi\) and \(\gamma\) denote the heading and flight path angles, respectively. \(J_{ij}(i=x,y,z;j=x,y,z)\) denotes the moment of inertia, \(M_{i}(i=x,y,z)\) is the external lumped moment, and \(\omega_{\text{E}}\) is the Earth's rotation velocity. Equation (1) can be written as  
\[\left\{ \begin{array}{l}\dot{\mathbf{\Lambda}}=\mathbf{R}\mathbf{\omega}+\mathbf{f}\\ \mathbf{J}\dot{\omega}=\mathbf{\Omega}\mathbf{\omega}+\mathbf{M}_{air}+\mathbf{M}_{c}+\Delta\mathbf{d} \end{array} \right., \tag{2}\]  
where \(\mathbf{\Lambda}=[\alpha,\beta,\sigma]^{\text{T}}\), and \(\mathbf{\omega}=[p,q,r]^{\text{T}}\). \(\Delta\mathbf{d}\) represents the external disturbances and parameter uncertainties. The inertia matrix is \(\mathbf{J}\in\mathbb{R}^{3\times 3}\), while \(\mathbf{M}_{c}\in\mathbb{R}^{3}\) denotes the control moment. The matrices \(\mathbf{R}\) and \(\mathbf{\Omega}\) and the aerodynamic moment \(\mathbf{M}_{air}\), are represented as  
\[\mathbf{R}= \begin{bmatrix}-\cos\alpha\tan\beta&1&-\sin\alpha\tan\beta\\ \sin\alpha&0&-\cos\alpha\\ -\cos\alpha\cos\beta&-\sin\beta&-\sin\alpha\cos\beta\end{bmatrix} , \tag{3}\]  
\[\mathbf{\Omega}= \begin{bmatrix}0&r&-q\\ -r&0&p\\ q&-p&0\end{bmatrix} , \tag{4}\]\[\mathbf{M}_{air}=\left[ \begin{array}{c}\left(\frac{m^{\frac{r}{2}L_{r}}}{V^{\frac{r}{ 2}}}+m^{\frac{r}{2}}_{r}\beta\right)q_{0}S_{r}L_{r}\\ \left(\frac{m^{\frac{r}{2}L_{r}}}{V}+m^{\frac{r}{2}}_{r}\beta\right)q_{0}S_{r}L _{r}\\ \left(\frac{m^{\frac{r}{2}L_{r}}}{V}+m^{\frac{r}{2}}_{r}\beta\right)q_{0}S_{r}L _{r}\\ \end{array} \right], \tag{5}\]  
where the air density is \(\rho\), and \(V\) is the velocity of RLV. \(m^{\beta}_{x}\), \(m^{\alpha}_{y}\), and \(m^{\beta}_{z}\) are the static stability moment coefficients of RLV; the damping moment coefficients are \(m^{p}_{x}\), \(m^{q}_{y}\), and \(m^{r}_{z}\), \(q_{0}=0.5\rho V^{2}\). The reference area of RLV is denoted as \(S_{r}\), and the reference length of RLV is denoted as \(L_{r}\). **Notation 1**.