# 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.
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Posted 6 years ago
 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.