I have a mathematical problem concerning a topic from control engineering.
For this purpose I have a (state) differential equation.
$\dot{x}=Ax+Bu$
$A=\begin{pmatrix} a_{11} &a_{12}&a_{13}&a_{14}\\ a_{21} &a_{22}&a_{23}&a_{24}\\ a_{31} &a_{32}&a_{33}&a_{34}\\ a_{41} &a_{42}&a_{43}&a_{44}\\ \end{pmatrix}$
$B=\begin{pmatrix} b_1\\ b_2\\ b_3\\ b_4 \end{pmatrix}$
Default is: $x=\begin{pmatrix} x_1\\ x_2\\ x_3\\ x_4 \end{pmatrix}$
For my application the vector shall be
$x=\begin{pmatrix} x_1\\ x_3\\ x_2\\ x_4 \end{pmatrix}$ What effect does this have on the overall differential equation? How must the A and B matrix be constructed? Do I need to swap only the rows or the columns?
What is the procedure? I ask for your help.
Thank you in advance and I appreciate any reply.
With kind regards