How to derive equations from Matlab lookup table data?

I want to analyze the stability of a simulink model. I happened to have 3-D lookup tables in my model. I have two questions regarding the subject matter. 1. Is there a possibility in matlab to write the equations based on the lookup table? If it is not available, what is the recommended method to derive the equations from the table data? 2. How to linearize the lookup table data? Because I want to implement LTI stability analysis techniques to my model. Thanks

Answer 1

[John D'Errico]

No. Sorry, but no. In general it is not possible to come up with a set of "equations" that represent any general relationship. For example, suppose I gave you a set of random numbers? What equation represents those numbers?

If you know a proper model that you expect the relationship to follow, then you can use a linear or nonlinear regression to estimate the parameters for that model. But that requires you to know something about the process, and to have a viable model for that process.

Usually at best you can use an interpolant, so in 3 dimensions, something like interp3 or interpn.

[Walter Roberson]

There are an infinite number of equations that fit any finite set of data, and there is no way to say that one set of equations is more right than the other.

If you specify a particular interpolation then any equations so formed would need to be in the form of piecewise representations or Heaviside or equivalent representations, where you can write a "formula" but the formula tends to be pretty obscure.