Exponential terms in numerator and denominator in a Transfer Function

I have the LTI system in the attachement and written below. Though, I am having difficulties typing it into Matlab. Is this possible with the exponentials?

num=exp(sqrt(s/alpha)*H)+exp(sqrt(s/alpha)*H)

den=A*R*(k*sqrt(s/alpha)+h_surface)*(exp(sqrt(s/alpha)*H)-exp(-sqrt(s/alpha)*H)

Please see the attachement for a clearer figure.

Thank you

Answer 1

[Jesús Zambrano]

Hi Jacob,

First please check that the transfer function is linear and time invariant. Most likely is not linear. For a system to be linear means that changing the input in a linear way will change the output in the same linear way. So if the input x1(t) produces the output y1(t) and the input x2​(t) produces the output y2​(t), then linear combinations of those inputs will produce linear combinations of those outputs.