Not exactly state transfer matrix, but sort of what you ask, you can see this if you like that is on constructing discrete time linear systems from given solutions. Check the examples that are included and you will immediately understand the notion. This is for homogeneous systems though, so it might not be what you ask for.

Data On the Modeling of Discrete Time Auto-Regressive Representations

Dear Lazaros,

thanks for the assistance, but I do not think it is what I am looking for.I may expect some thing a bit similar to "Bar-Shalom Y. Optimal Simultaneous State Estimation And Parameter Identification In Linear Discrete-Time Systems.[J]. IEEE Transactions on Automatic Control, 2010, 17(3):142.".

zhuang