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

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

You can also check if it is included in the Slicot library at 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

Hi Zdenek,

Thanks a lot for your help!!!!! I really appreciate it ^__^

Regards,

Richard

Zdenek Hur=E1k wrote: