system,model ,model equations, estimate A,B,C,D,X from system,
any book,video or practical example that generate data and estimate states it is linear time invariant system thanks.
You can see the paper "State and parameter estimation: a nonlinear Luenberger approach"
in which an observer is used to estimate both state and parameters of a linear model.
If your goal is only to find the matrices A,B,C,D you can use least-square minimisation technique based
on your data 'y' and 'u'.
For this, you can fix the order of your model and use one of the controlable or observable canonical forms to represent it.
After that, solve the optimization problem (by using, e.g., fmincon function of Matlab) to find the entries of the matrices
Ac,Bc,Cc,Dc corresponding to one of the canonical forms.
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