$$ Z = \Delta X = X-X^\ X = Z+X^\
\dot{X} = \dot{Z}\ \dot{X} = \left. \begin{bmatrix} \frac{\partial f_1}{\partial x_1} & \frac{\partial f_1}{\partial x_2}\ \frac{\partial f_2}{\partial x_1} & \frac{\partial f_1}{\partial x_2} \end{bmatrix}\right|{X^,F^} Z+\left. \begin{bmatrix} \frac{\partial f_1}{\partial u}\ \frac{\partial f_2}{\partial u} \end{bmatrix}\right|{X^,F^} u\
% \dot{X} = \left. % \begin{bmatrix} % \frac{\partial f_1}{\partial x_1} & \frac{\partial f_1}{\partial x_2}\ % \frac{\partial f_2}{\partial x_1} & \frac{\partial f_1}{\partial x_2} % \end{bmatrix}\right|{X^,F^} % (X-X^*)+\left. % \begin{bmatrix} % \frac{\partial f_1}{\partial u}\ % \frac{\partial f_2}{\partial u} % \end{bmatrix}\right|{X^,F^} % u\
% \dot{X} = \left. % \begin{bmatrix} % \frac{\partial f_1}{\partial x_1} & \frac{\partial f_1}{\partial x_2}\ % \frac{\partial f_2}{\partial x_1} & \frac{\partial f_1}{\partial x_2} % \end{bmatrix}\right|{X^,F^} % X- % \left. % \begin{bmatrix} % \frac{\partial f_1}{\partial x_1} & \frac{\partial f_1}{\partial x_2}\ % \frac{\partial f_2}{\partial x_1} & \frac{\partial f_1}{\partial x_2} % \end{bmatrix}\right|{X^,F^}X^* + \left. % \begin{bmatrix} % \frac{\partial f_1}{\partial u}\ % \frac{\partial f_2}{\partial u} % \end{bmatrix}\right|_{X^,F^} % u\
% \dot{X} = \left. % \begin{bmatrix} % \frac{\partial f_1}{\partial x_1} & \frac{\partial f_1}{\partial x_2}\ % \frac{\partial f_2}{\partial x_1} & \frac{\partial f_1}{\partial x_2} % \end{bmatrix}\right|{X^,F^} % X + \left. % \begin{bmatrix} % \frac{\partial f_1}{\partial u}\ % \frac{\partial f_2}{\partial u} % \end{bmatrix}\right|{X^,F^} % u- % \left. % \begin{bmatrix} % \frac{\partial f_1}{\partial x_1}x_1^* & \frac{\partial f_1}{\partial x_2}x_2^\ % \frac{\partial f_2}{\partial x_1}x_1^ & \frac{\partial f_1}{\partial x_2} x_2^* % \end{bmatrix}\right|_{X^,F^} $$