Convert Differential Equations to Spate Space

I have a system of differential equations, which I would like to convert to spate-space representation:

s = [x(2);
    (x(4)*x(6)*(p.Iyy-p.Izz)-(u(1)+u(2)+u(3)+u(4))*p.IR*x(4)...
    +(p.b*p.l*(u(2)^2-u(4)^2)))/p.Ixx; 
    x(4);  
    (x(2)*x(6)*(p.Izz-p.Ixx)+(u(1)+u(2)+u(3)+u(4))*p.IR*x(2)...
    +(p.b*p.l*(u(3)^2-u(1)^2)))/p.Iyy; 
    x(6);  
    (x(4)*x(2)*(p.Ixx-p.Iyy)+(p.d*(u(1)^2+u(3)^2-u(2)^2-u(4)^2)))/p.Izz; 
    x(8); 
    ((p.b*(u(1)^2+u(2)^2+u(3)^2+u(4)^2))*(sin(x(1))*sin(x(5))...
    +cos(x(1))*sin(x(3))*cos(x(5))))/p.mass;
    x(10); 
    ((p.b*(u(1)^2+u(2)^2+u(3)^2+u(4)^2))*(cos(x(1))*sin(x(3))*sin(x(5))...
    -sin(x(1))*cos(x(5))))/p.mass; 
    x(12); 
    ((p.b*(u(1)^2+u(2)^2+u(3)^2+u(4)^2))*(cos(x(1))*cos(x(3)))-p.mass*p.g)/p.mass];

The confusing moment for me is that there are multiplication of state variables (e.g. x(4)*x(6)), so I don't know how to write it down in A matrix.

Is it possible to convert such system to state-space? Could you hint the way how it should look like?

Thank you in advance for your answer!

Answer 1

[Star Strider]

In order to convert your equations to a state-space representation, you need to linearise them. This involves taking the Jacobian. I refer you to Linearization of Nonnlinear Systems to guide your efforts. The Symbolic Math Toolbox (that was not available when I encountered this) can likely help you significantly.

There are several other such references that reveal themselves in an Interweb search.

[pozmogov]

Thank you very much for your answer! Really helpful.

[Star Strider]

As always, my pleasure!