how to create a state-space model without disturbance

Question

how to create a state-space model without disturbance and how does the disturbance influence the solution I would like to identify parameters of an ODE using the system identification toolbox. The sate-space representation in MATLAB is always formulated with a disturbance e, which always influences the solution y due to the equation y = Cx + Dy + e. In my problem, there is no disturbance present. Now, I have two questions: - Of which form is the disturbance e and in which way does it influence the solution (setting K = 0) - Is there the possibility to describe a state-space model in MATLAB without disturbance

Kshitij Singh · Accepted Answer

The difference between the output of the model and the actual (measured) output is, in general, not going to be zero. So, there will be an error e such that:
 e = ymeasured-ymodel,
where
 ymodel = Cx + Du
which means:
 ymeasured = Cx + Du + e
When you set K = 0 in the idss model, the parameters you get by minimizing |e||| are the ODE coefficients you are interested in. Furthermore, using
 [A, B, C, D] = ssdata(model)
you can extract out the state-space coefficients of the output-reproducing model: xdot = Ax + Bu; y = Cx+du

how to create a state-space model without disturbance

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