When the parameters of a state space model change, the states calculated are believed to "change" accordingly, but how do they change? The statistics will change or are there some other ways to "measure" the difference with the states if the parameters remain the same? Besides, how can we tell which of the parameters have changed according to the states?
hi
you must be attention to 2 issues
1- the realtion between states and input/output, we discuss this issue in controlability and observability of state
2- the relation between the state (ODE & DAE)
i suggest research about equvalence models in state space
you can find basic of this issue in modern control of CHENG
Your question is not clear. When you have a time varying state space model, then you must have a way of computing the parameter matrices. There are mutually interactive state and parameter estimation algorithms that alternate between state estimation and parameter estimation. However, if your model is supposed to be time invariant, then you need not compute the parameters, but if the performance starts to degrade (i.e., your output is not following the measured output), then you might need to update the model.
Note that you can formulate the problem as a state estimation problem with fixed parameters, then use the estimated states as fixed and estimate the parameters. This is done in an iterative fashion. Then you will know how all parameters are changing.
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