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The state-space model in Mathematica

Posted 6 years ago
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Hello.

I would like to know how mathematica's state-space works as the description and examples the have at https://reference.wolfram.com/language/ref/StateSpaceModel.html isn't very helpful.

Thank you.

3 Replies

Are you looking for documentation for Mathematica or for Wolfram SystemModeler?

Are you looking for:

How to see the output of a StateSpaceModel? https://reference.wolfram.com/language/ref/OutputResponse.html

How to join StateSpaceModels together? https://reference.wolfram.com/language/ref/SystemsModelSeriesConnect.html https://reference.wolfram.com/language/ref/SystemsModelParallelConnect.html

Describe the StateSpaceModel as a TransferFunction?: https://reference.wolfram.com/language/ref/TransferFunctionModel.html

Posted 6 years ago

I was referring to the state space model function.

I have attached an example.

I would like to know what each part of the matrix output is.

Attachments:

StateSpaceModel[{a,b,c,d}] represents the following equation:

x' = a x + b u
y  = c x + d u

where a,b,c,d are matrices.

Each of the four matrices (a,b,c,d) are themselves put together in a matrix of sorts, with lines to separate the the matrices. The are arranged in the same order they appear in the equation above

a b
c d

So in your example, "d" is just the matrix/scalar 0. "c" the horizontal matrix/vector at the bottom left. "b" is the vertical matrix/vector starting at the top right. And "a" is the square matrix starting at the top left that takes up most of the output.

The "S" at the very top right is just to denote that the arrangement of numbers is a StateSpaceModel and not an actual matrix.

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