Hello

My experience with the symbolic toolbox of MATLAB says that it is incapable of doing such inversion.

The first solution is to try to design a controller in state-space, instead of the Laplace domain.

Besides, since your system is large and as long as there exists no physical linear system, I think it is better to design nonlinear a control law for the original system.

Regards,

You may find this useful for you

https://www.mathworks.com/help/symbolic/ilaplace.html

What you are trying to do is following:

syms s;

A = rand(24);

STM = ilaplace(inv(s*eye(size(A))-A)); % This is state-transition matrix

This code will work, but will consume some amount of time. If you want to calculate STM, better way is to do it numerically rather than computing symbolically. My recommendation is to use the following property of STM:

d/dt(STM) = A*STM, with initialization as STM(t=0) = identity matrix of size of A.

You can easily solve this matrix differential equation using any ode solver, or may be in Simulink. This will give faster result than symbolic calculation.