How to get generalized plant model in state space (A,B1,B2,C​1,D11,D12,​C2,D21,D22​) using augw command?

I would like to obtain the generalized plant model in state space format from the result after running the augw command. I know how to run augw and the format of augmented plant P(s) in this link: https://www.mathworks.com/help/robust/ref/lti.augw.html. However, I am not sure about how to find the specific values of matrices of (A,B1,B2,C1,D11,D12,C2,D21,D22) from the property of augmented P matrix. Can somebody explain how to get the above matrices from the following results?

Answer 1

[Paul]

Does this Answer help?

[TASI IUPUI]

Hi Paul, thanks a lot for your reply. I checked you aswer and it is helpful. However, the augmented matrix P generated using command augw is not the same condition as what you did before. This is because the methods of generaing the new state-space model (A,B,C,D) are different.

In this new condition, we have the augmented system model P with four system matrices (A,B,C,D), but we cannot use the partition you showed since the new A (12 states) is different with my original system matrix A (4 states). It seems like I need to extract (A, B1, B2, C1,...) from the above big 4 matrices. I am really not sure about how to implement this partitioning?

Thank you so much!

[Paul]

It seems to me that the augmented plant, P, is exactly the same as in that Answer with the following mappings between the input/output groups of P and the i/o signals shown on the doc page for augw (I wonder why P doesn't use the same signal names as on the doc page?).

U1 -> w

U2 -> u

Y1 -> z

Y2 - e (which I called y in that other Answer)

So the augmented plant, P, has n=12 states, and w is a vector of nw=4 inputs, and u is vector of nu=1 inputs, and z is vector of nz=9 outputs, y (or e) is vector of ny=4 outputs.

Does that sound right for your problem?

[TASI IUPUI]

Hi Paul thanks, in the previous answer, we firstly supposed to have the generalized model below:

xdot = A*x + B1*w + B2*u

z = C1*x + D11*w + D12*u

y = C2*x + D21*w + D22*u

And then try to obtain the matrices from the obtained state-space model by partitioning from A,B,C,D.

But now I try to derive this generalized plant model by designing the weighting matrices W1, W2, and W3 from a normal state-space model below:

xdot = A*x + Bu

y = C*x + D*u

Thus, I am now checking whether the command augw can give me a correct way to get that.