Depending on the eigenvalues (and in fact eigenvectors) of A and B, not all entries of A are equally important in evolving the system states of (A,B). In fact, it seems that some entries in A, e.g. a_(ij), with some proper mapping could be zero because the effect of x_j on x_i is quite negligible as time proceeds. The problem is for a stable (or marginally stable) A how that mapping is defined to maximize the number of zero entries in A_s. I am interested in knowing all related results for this problem. 

I do not care if you know of some results on continuous-time systems.

Thanks in advance.