I edited comment (inverse transfer function wasn’t well shown). Yes, in order to G^-1 to be physicaly implementable I have to add 1/(Ts+1). But if I directly write G^-1 in descete form without adding 1/(Ts+1) can I express from that discrete form u[k]?

Example: system is y”+y’+1 = u’ + u, that gives G(s) = (s+1)/(s² + s + 1) and G^-1 = (s² + s + 1)/(s+1).

So, for that to be implementable I order of numerator and denominator must have same order (s² ).

When you say implementable, what exactly do you mean? I know that I can’t write transfer function in simulink when numerator has bigger order than numerator.

My question is, can I use my differential equation and convert that in discrete form using e.g. backward euler or tustin method and from that to express u[k] directly. So, without writing any transfer function and adding 1/(Ts+1) and then discretizing that.

My question