state simulation error

Hello everyone, I am wondering if anyone knows if there is any theoretical analysis of the following problem:     Given a LTI continuous model, its system matrices(A,B)'s structure
are known. In saying so, I mean the dimension, the location of zeor entries in the matrix. But not all the nonzero entries are known. Also known are the input (u) and a state measurement say, x1.     By fitting the model to the u/x1 pair, one obtains A_hat and B_hat, which are not necessarily equal to (A,B). Then the question is under what condition, other states simulated with A_hat and B_hat will be close to their true values given x1_hat close to x1.
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