The problem is as follows. Given a model, a set of initial conditions X(0) and a time horizon N, we want to compute the states reachable at time 1, 2, ..., N. In other words, we want to determine X(1), X(2), ..., X(N).
The model is a class of discrete-time PWA systems:
x(k+1) = A_i x(k) + b_i, if x(k) \in R_i where i \in {1,...,M}
For each i \in {1,...,M}, there is a single element in each row of matrix A_i with the value of 1 and the others are 0.
