How can I establish the system equation of such a control algorithm

I am working on a dynamic model of a 2-wheel differential drive mobile robot. And I try to implement a control algorithm of one published paper. In the paper, there is a control algorithm for path following. I just want to re-implement that via Matlab. The diagram of control algorithm was presented in the paper. But I don't know how I can establish the system equations like:

dot(x) = Ax + Bu

y = Cx + Du

I want to know these equations just because I want to implement the linear feedback of the control algorithm which is unknown and not presented in the paper. I put a figure of that below. Could anyone helps me?