Finding Matrix A from Dynamics x'=Ax

[shaner-baner]

I am working with a system governed by the dynamics x'=Ax (prime denotes differentiation w/ respect to t) where x is a vector and A is a matrix. Given the way our data is collected we can't measure x directly but rather a scalar function D(x)=(sum of the components of the vector x). My question is: given sufficiently many data points what can we conclude about the matrix A? Can we find its entries uniquely or are we stuck with a set of infinitely many solutions? And finally how does the answer to this question depend on the structure of the matrix (distinct/repeated eigenvalues etc.)

 

[neurocomp2003]

all you have is the D(x)=sum(x_i)? are you given x'?