Suppose we acknowledge $q_{i-1}$ as an independent signal, then using the block diagram, the following equations can be derived:
$$e_i = d_i - d_{r,i} = - q_i+q_{i-1} - d_{r,i}$$
$$q_i = G_i(s)u_i = PDG_i(s)e_i$$
substitute the first in the latter:
$$q_i = PDG_i(s)(- q_i+q_{i-1} - d_{r,i})$$
$$(1+PDG_i(s))q_i = PDG_i(s)(q_{i-1} - d_{r,i})$$
$$q_i = \frac{PDG_i(s)}{1+PDG_i(s)}(q_{i-1} - d_{r,i})$$
Which represents a transferfunction with $(q_{i-1} - d_{r,i})$ as input and $q_i$ as output. The troublesome part here is this $q_{i-1}$, of which I do not know its meaning (is $i$ a discrete time index, or is $q$ a set of systems where $q_i$ is an part of it).
Even thought one could substitute
$$q_{i-1} = \frac{PDG_{i-1}(s)}{1+PDG_{i-1}(s)}(q_{i-2} - d_{r,i-1})$$
into the equation, the problem is only shifted to $q_{i-2}$ and so on. As such, the complete transfer matrix (where the input is every instance of $d_{r,i-n}$ and the output is every instance of $q_{i-n}$) will be the full definition of your system. However, if $i$ is a discrete time index, you could try to convert the model and controller to the Z domain and describe $q_{i-1} = z^{-1}q_i $
