3 state space model time discretization

I am trying to create a 3-state space model of the adaptive cruise control as following

and discretize the model

however, the state-space function [ss(A,B,C,D)] of matlab defaulted to

and system

and I can't create the state space mode.

How can I create the 3-state space model manually?

Answer 1

[Torsten]

x_dot = A*x + [B,C]*[u;v]

So define

A_ss = A, B_ss = [B,C]