# Conversion from multivariable ARX model to multivariable State-Space model using MATLAB

Hi,
Does MATLAB convert MIMO ARX model to MIMO State-Space model (and vice versa)? If yes, what is the command? I am not able to find it. I am
currently using 6.5.1.199709 (R13) Service Pack 1.
Thanks a lot!
Richard
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Hi Richard,
Richard wrote:

If I understand your needs right, you have a model of a MIMO system in the format
D(d)y(k)=N(d)u(k)
and you would like to find an equivalent state-space model
xdot(k) = Ax(k)+Bu(k) y(k) = Cx(k)+Du(k)
what you need is a routine for conversion between polynomial matrix fraction D^-1N and state-space format. As far as I know, there is none in Control System Toolbox for Matlab. This routine is included in a commercial Polynomial Toolbox distributed by http://www.polyx.com . You can also check if it is included in the Slicot library at http://www.slicot.de . Some functionality for polynomial matrices is also covered in Scilab, as far as I know.
In Polynomial Toolbox, the typical session looks like this:

A -0.64 - 0.56d + 0.44d^2 -0.95 + 0.78d + 0.57d^2 -0.82 - 0.27d - 1.2d^2 -2.2 + 0.99d - 0.52d^2 B 0.23 + 0.021d -1 - 0.95d

a x1 x2 x3 x4 x1 -1.583 1 1.266 0 x2 3.401 0 2.82 0 x3 0.4702 0 -0.02444 1 x4 -1.808 0 -1.288 0 b u1 x1 3.926 x2 -4.29 x3 -0.1479 x4 2.565 c x1 x2 x3 x4 y1 1 0 0 0 y2 -0 0 1 0 d u1 y1 -2.374 y2 1.341 Sampling time: 1 Discrete-time model.
Best regards, Zdenek
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Hi Zdenek,
Thanks a lot for your help!!!!! I really appreciate it ^__^
Regards,
Richard
Zdenek Hur�k wrote: