I have some input-output data for a dynamical system (input = stimulus, output = observation). Assuming that this system is linear time-invariant, I am trying to estimate a transfer function $H(s)$ of this system in MATLAB. I found the function tfest in the System Identification Toolbox. It allows you to define the number of poles, the number of zeros, and even some delay.
However, I am wondering if it is possible to force the transfer function to have a certain structure. For example, $$H(s) = H_1(s) + \alpha \, e^{-\tau s} \, H_2(s).$$
Is there a way to estimate this structured transfer function in Matlab?
Thank you in advance for your help.